Characters Of Finite Coxeter Groups And Iwahori Hecke Algebras

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Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras

Author : Meinolf Geck
Publisher : Oxford University Press
ISBN 13 : 9780198502500
Total Pages : 478 pages
Book Rating : 4.5/5 (25 download)

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Book Synopsis Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras by : Meinolf Geck

Download or read book Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras written by Meinolf Geck and published by Oxford University Press. This book was released on 2000 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.

Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group

Author : Andrew Mathas
Publisher : American Mathematical Soc.
ISBN 13 : 0821819267
Total Pages : 204 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group by : Andrew Mathas

Download or read book Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group written by Andrew Mathas and published by American Mathematical Soc.. This book was released on 1999 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.

Handbook of Algebra

Author : M. Hazewinkel
Publisher : Elsevier
ISBN 13 : 0080462499
Total Pages : 543 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Algebra by : M. Hazewinkel

Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2006-05-30 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes

The Character Theory of Finite Groups of Lie Type

Author : Meinolf Geck
Publisher : Cambridge University Press
ISBN 13 : 1108489621
Total Pages : 405 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis The Character Theory of Finite Groups of Lie Type by : Meinolf Geck

Download or read book The Character Theory of Finite Groups of Lie Type written by Meinolf Geck and published by Cambridge University Press. This book was released on 2020-02-27 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.

Representations of Hecke Algebras at Roots of Unity

Author : Meinolf Geck
Publisher : Springer Science & Business Media
ISBN 13 : 0857297163
Total Pages : 410 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Representations of Hecke Algebras at Roots of Unity by : Meinolf Geck

Download or read book Representations of Hecke Algebras at Roots of Unity written by Meinolf Geck and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.

Computer Algebra Handbook

Author : Johannes Grabmeier
Publisher : Springer Science & Business Media
ISBN 13 : 3642558267
Total Pages : 656 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Computer Algebra Handbook by : Johannes Grabmeier

Download or read book Computer Algebra Handbook written by Johannes Grabmeier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Combinatorics of Coxeter Groups

Author : Anders Bjorner
Publisher : Springer Science & Business Media
ISBN 13 : 3540275967
Total Pages : 371 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Combinatorics of Coxeter Groups by : Anders Bjorner

Download or read book Combinatorics of Coxeter Groups written by Anders Bjorner and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Representations of Reductive Groups

Author : Monica Nevins
Publisher : Birkhäuser
ISBN 13 : 3319234439
Total Pages : 545 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Representations of Reductive Groups by : Monica Nevins

Download or read book Representations of Reductive Groups written by Monica Nevins and published by Birkhäuser. This book was released on 2015-12-18 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Representations of Finite Groups of Lie Type

Author : François Digne
Publisher : Cambridge University Press
ISBN 13 : 1108642128
Total Pages : 267 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Representations of Finite Groups of Lie Type by : François Digne

Download or read book Representations of Finite Groups of Lie Type written by François Digne and published by Cambridge University Press. This book was released on 2020-03-05 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.

Representation Theory of Finite Reductive Groups

Author : Marc Cabanes
Publisher : Cambridge University Press
ISBN 13 : 0521825172
Total Pages : 457 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Representation Theory of Finite Reductive Groups by : Marc Cabanes

Download or read book Representation Theory of Finite Reductive Groups written by Marc Cabanes and published by Cambridge University Press. This book was released on 2004-01-29 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Representation Theory of Algebraic Groups and Quantum Groups

Author : Akihiko Gyoja
Publisher : Springer Science & Business Media
ISBN 13 : 0817646973
Total Pages : 356 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Representation Theory of Algebraic Groups and Quantum Groups by : Akihiko Gyoja

Download or read book Representation Theory of Algebraic Groups and Quantum Groups written by Akihiko Gyoja and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Groups, Graphs and Random Walks

Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 1316817784
Total Pages : 539 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Groups, Graphs and Random Walks by : Tullio Ceccherini-Silberstein

Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.

Infinite-Dimensional Aspects of Representation Theory and Applications

Author : Stephen Berman
Publisher : American Mathematical Soc.
ISBN 13 : 082183701X
Total Pages : 168 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Infinite-Dimensional Aspects of Representation Theory and Applications by : Stephen Berman

Download or read book Infinite-Dimensional Aspects of Representation Theory and Applications written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2005 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Modular Representation Theory Of Finite And P-adic Groups

Author : Wee Teck Gan
Publisher : World Scientific
ISBN 13 : 9814651826
Total Pages : 277 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Modular Representation Theory Of Finite And P-adic Groups by : Wee Teck Gan

Download or read book Modular Representation Theory Of Finite And P-adic Groups written by Wee Teck Gan and published by World Scientific. This book was released on 2015-02-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author : Gebhard Böckle
Publisher : Springer
ISBN 13 : 3319705660
Total Pages : 753 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by : Gebhard Böckle

Download or read book Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory written by Gebhard Böckle and published by Springer. This book was released on 2018-03-22 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Categorification and Higher Representation Theory

Author : Anna Beliakova
Publisher : American Mathematical Soc.
ISBN 13 : 1470424606
Total Pages : 376 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Categorification and Higher Representation Theory by : Anna Beliakova

Download or read book Categorification and Higher Representation Theory written by Anna Beliakova and published by American Mathematical Soc.. This book was released on 2017-02-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory. The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.

Characters of Reductive Groups Over a Finite Field

Author : George Lusztig
Publisher : Princeton University Press
ISBN 13 : 9780691083513
Total Pages : 412 pages
Book Rating : 4.0/5 (835 download)

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Book Synopsis Characters of Reductive Groups Over a Finite Field by : George Lusztig

Download or read book Characters of Reductive Groups Over a Finite Field written by George Lusztig and published by Princeton University Press. This book was released on 1984-06-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups.