Representations Of Affine Hecke Algebras

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Iwahori-Hecke Algebras and Their Representation Theory

Author : Ivan Cherednik
Publisher : Springer Science & Business Media
ISBN 13 : 9783540002246
Total Pages : 132 pages
Book Rating : 4.0/5 (22 download)

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Book Synopsis Iwahori-Hecke Algebras and Their Representation Theory by : Ivan Cherednik

Download or read book Iwahori-Hecke Algebras and Their Representation Theory written by Ivan Cherednik and published by Springer Science & Business Media. This book was released on 2002-12-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Double Affine Hecke Algebras

Author : Ivan Cherednik
Publisher : Cambridge University Press
ISBN 13 : 0521609186
Total Pages : 449 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Double Affine Hecke Algebras by : Ivan Cherednik

Download or read book Double Affine Hecke Algebras written by Ivan Cherednik and published by Cambridge University Press. This book was released on 2005-03-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

Affine Hecke Algebras and Orthogonal Polynomials

Author : I. G. Macdonald
Publisher : Cambridge University Press
ISBN 13 : 9780521824729
Total Pages : 200 pages
Book Rating : 4.8/5 (247 download)

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Book Synopsis Affine Hecke Algebras and Orthogonal Polynomials by : I. G. Macdonald

Download or read book Affine Hecke Algebras and Orthogonal Polynomials written by I. G. Macdonald and published by Cambridge University Press. This book was released on 2003-03-20 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.

Representations of Affine Hecke Algebras

Author : Nanhua Xi
Publisher : Springer
ISBN 13 : 3540486828
Total Pages : 147 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Representations of Affine Hecke Algebras by : Nanhua Xi

Download or read book Representations of Affine Hecke Algebras written by Nanhua Xi and published by Springer. This book was released on 2006-11-15 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

Lie Groups, Geometry, and Representation Theory

Author : Victor G. Kac
Publisher : Springer
ISBN 13 : 3030021912
Total Pages : 545 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Lie Groups, Geometry, and Representation Theory by : Victor G. Kac

Download or read book Lie Groups, Geometry, and Representation Theory written by Victor G. Kac and published by Springer. This book was released on 2018-12-12 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)

Reflection Groups and Coxeter Groups

Author : James E. Humphreys
Publisher : Cambridge University Press
ISBN 13 : 9780521436137
Total Pages : 222 pages
Book Rating : 4.4/5 (361 download)

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Book Synopsis Reflection Groups and Coxeter Groups by : James E. Humphreys

Download or read book Reflection Groups and Coxeter Groups written by James E. Humphreys and published by Cambridge University Press. This book was released on 1992-10 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

Hecke Algebras with Unequal Parameters

Author : George Lusztig
Publisher : American Mathematical Soc.
ISBN 13 : 0821833561
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hecke Algebras with Unequal Parameters by : George Lusztig

Download or read book Hecke Algebras with Unequal Parameters written by George Lusztig and published by American Mathematical Soc.. This book was released on 2003 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.

Representation Theory of Algebraic Groups and Quantum Groups

Author : Toshiaki Shoji
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Representation Theory of Algebraic Groups and Quantum Groups by : Toshiaki Shoji

Download or read book Representation Theory of Algebraic Groups and Quantum Groups written by Toshiaki Shoji and published by American Mathematical Society(RI). This book was released on 2004 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.

Linear and Projective Representations of Symmetric Groups

Author : Alexander Kleshchev
Publisher : Cambridge University Press
ISBN 13 : 1139444069
Total Pages : 293 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Linear and Projective Representations of Symmetric Groups by : Alexander Kleshchev

Download or read book Linear and Projective Representations of Symmetric Groups written by Alexander Kleshchev and published by Cambridge University Press. This book was released on 2005-06-30 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own

Lie Algebras of Finite and Affine Type

Author : Roger William Carter
Publisher : Cambridge University Press
ISBN 13 : 9780521851381
Total Pages : 662 pages
Book Rating : 4.8/5 (513 download)

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Book Synopsis Lie Algebras of Finite and Affine Type by : Roger William Carter

Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.

The Admissible Dual of GL(N) Via Compact Open Subgroups

Author : Colin John Bushnell
Publisher : Princeton University Press
ISBN 13 : 9780691021140
Total Pages : 330 pages
Book Rating : 4.0/5 (211 download)

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Book Synopsis The Admissible Dual of GL(N) Via Compact Open Subgroups by : Colin John Bushnell

Download or read book The Admissible Dual of GL(N) Via Compact Open Subgroups written by Colin John Bushnell and published by Princeton University Press. This book was released on 1993 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N, F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.

Ring Theory 2019 - Proceedings Of The Eighth China-japan-korea International Symposium On Ring Theory

Author : Hideto Asashiba
Publisher : World Scientific
ISBN 13 : 9811230307
Total Pages : 256 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Ring Theory 2019 - Proceedings Of The Eighth China-japan-korea International Symposium On Ring Theory by : Hideto Asashiba

Download or read book Ring Theory 2019 - Proceedings Of The Eighth China-japan-korea International Symposium On Ring Theory written by Hideto Asashiba and published by World Scientific. This book was released on 2021-01-04 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1991, the group of ring theorists from China and Japan, joined by Korea from 1995 onwards, took turns to hold the quadrennial international conferences (sometimes also referred to as symposiums). As the proceedings of the eighth conference held in Nagoya, Japan in 2019, this volume consists of a collection of articles by invited speakers (survey) and general speakers (survey and original), all of which were refereed by world experts.The survey articles show the trends of current research and offer clear, thorough explanations that are ideal for researchers also in other specialized areas of ring theory. The original articles display new results, ideas and tools for research investigations in ring theory.The articles cover major areas in ring theory, such as: structures of rings, module theory, homological algebra, groups, Hopf algebras, Lie theory, representation theory of rings, (non-commutative) algebraic geometry, commutative rings (structures, representations), amongst others.This volume is a useful resource for researchers — both beginners and advanced experts — in ring theory.

Representations of Algebraic Groups

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 082184377X
Total Pages : 594 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Algebraic Groups by : Jens Carsten Jantzen

Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Iwahori-Hecke Algebras and their Representation Theory

Author : Ivan Cherednik
Publisher : Springer
ISBN 13 : 3540362053
Total Pages : 117 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Iwahori-Hecke Algebras and their Representation Theory by : Ivan Cherednik

Download or read book Iwahori-Hecke Algebras and their Representation Theory written by Ivan Cherednik and published by Springer. This book was released on 2003-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Automorphic Forms on GL (3,TR)

Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump

Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representation Theories and Algebraic Geometry

Author : A. Broer
Publisher : Springer Science & Business Media
ISBN 13 : 9401591318
Total Pages : 455 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Representation Theories and Algebraic Geometry by : A. Broer

Download or read book Representation Theories and Algebraic Geometry written by A. Broer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Author : Jacob Greenstein
Publisher : Birkhäuser
ISBN 13 : 9783030638511
Total Pages : 0 pages
Book Rating : 4.6/5 (385 download)

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Book Synopsis Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification by : Jacob Greenstein

Download or read book Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification written by Jacob Greenstein and published by Birkhäuser. This book was released on 2023-03-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.