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Representation Theory Of The Symmetric Groups
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Book Synopsis The Representation Theory of the Symmetric Group by : Gordon Douglas James
Download or read book The Representation Theory of the Symmetric Group written by Gordon Douglas James and published by Cambridge University Press. This book was released on 1984-12-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras; and new uses are still being found.
Book Synopsis The Symmetric Group by : Bruce E. Sagan
Download or read book The Symmetric Group written by Bruce E. Sagan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
Book Synopsis Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize by : Sergei Vasilʹevich Kerov
Download or read book Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize written by Sergei Vasilʹevich Kerov and published by American Mathematical Soc.. This book was released on with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reproduces the doctoral thesis written by a remarkable mathematician, Sergei V. Kerov. His untimely death at age 54 left the mathematical community with an extensive body of work and this one-of-a-kind monograph. Here, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on an important topic of current research. Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of both directions. His book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram. He also studies stochastic properties of the deviations of random diagrams from the limiting curve. Among the problems of the second type, Kerov studies an important problem of computing irreducible characters of the infinite symmetric group. This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams. In turn, this construction provides a completely new description of the relation between the classical moment problems of Hausdorff and Markov. The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics.
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
Book Synopsis Representations of the Infinite Symmetric Group by : Alexei Borodin
Download or read book Representations of the Infinite Symmetric Group written by Alexei Borodin and published by Cambridge University Press. This book was released on 2017 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Book Synopsis Lambda-Rings and the Representation Theory of the Symmetric Group by : Donald Knutson
Download or read book Lambda-Rings and the Representation Theory of the Symmetric Group written by Donald Knutson and published by Lecture Notes in Mathematics. This book was released on 1973-03-06 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Book Synopsis Symmetry, Representations, and Invariants by : Roe Goodman
Download or read book Symmetry, Representations, and Invariants written by Roe Goodman and published by Springer Science & Business Media. This book was released on 2009-07-30 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.
Book Synopsis Representation Theory by : Amritanshu Prasad
Download or read book Representation Theory written by Amritanshu Prasad and published by Cambridge University Press. This book was released on 2015-02-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
Book Synopsis Projective Representations of the Symmetric Groups by : Peter Norman Hoffman
Download or read book Projective Representations of the Symmetric Groups written by Peter Norman Hoffman and published by Oxford University Press. This book was released on 1992 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the symmetric groups forms one of the basic building blocks of modern group theory. This book presents information currently known on the projective representations of the symmetric and alternating groups. Special emphasis is placed on the theory of Q-functions and skew Q-functions.
Book Synopsis The Theory of Group Characters and Matrix Representations of Groups by : Dudley Ernest Littlewood
Download or read book The Theory of Group Characters and Matrix Representations of Groups written by Dudley Ernest Littlewood and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.
Book Synopsis Representations of Finite and Compact Groups by : Barry Simon
Download or read book Representations of Finite and Compact Groups written by Barry Simon and published by American Mathematical Soc.. This book was released on 1996 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.
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.
Book Synopsis Integral Representations by : I. Reiner
Download or read book Integral Representations written by I. Reiner and published by Springer. This book was released on 2006-11-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations and Characters of Groups by : Gordon James
Download or read book Representations and Characters of Groups written by Gordon James and published by Cambridge University Press. This book was released on 2001-10-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
Book Synopsis Finite Permutation Groups by : Helmut Wielandt
Download or read book Finite Permutation Groups written by Helmut Wielandt and published by Academic Press. This book was released on 2014-05-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
