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Genre | : Mathematics |
Author | : G.D. James |
Publisher | : Springer |
Release | : 2006-11-15 |
File | : 162 Pages |
ISBN-13 | : 9783540357117 |
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Genre | : Mathematics |
Author | : G.D. James |
Publisher | : Springer |
Release | : 2006-11-15 |
File | : 162 Pages |
ISBN-13 | : 9783540357117 |
The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.
Genre | : Mathematics |
Author | : Tullio Ceccherini-Silberstein |
Publisher | : Cambridge University Press |
Release | : 2010-02-04 |
File | : 429 Pages |
ISBN-13 | : 9781139483964 |
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
Genre | : Mathematics |
Author | : Pierre-Loic Meliot |
Publisher | : CRC Press |
Release | : 2017-05-12 |
File | : 433 Pages |
ISBN-13 | : 9781315353852 |
Introducing the representation theory of finite groups, this second edition has been revised and updated. The theory is developed in terms of modules with considerable emphasis placed upon constructing characters.
Genre | : Mathematics |
Author | : Gordon Douglas James |
Publisher | : Cambridge University Press |
Release | : 2001-10-18 |
File | : 476 Pages |
ISBN-13 | : 052100392X |
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
Genre | : Mathematics |
Author | : Alexander Kleshchev |
Publisher | : Cambridge University Press |
Release | : 2005-06-30 |
File | : 293 Pages |
ISBN-13 | : 9781139444064 |
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.
Genre | : Mathematics |
Author | : Andrew Mathas |
Publisher | : American Mathematical Soc. |
Release | : 1999 |
File | : 204 Pages |
ISBN-13 | : 9780821819265 |
Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Genre | : Mathematics |
Author | : Ronald Solomon |
Publisher | : Walter de Gruyter |
Release | : 2012-05-02 |
File | : 164 Pages |
ISBN-13 | : 9783110806298 |
The Representation Theory of Finite Groups
Genre | : Computers |
Author | : W. Feit |
Publisher | : Elsevier |
Release | : 1982-05-01 |
File | : 517 Pages |
ISBN-13 | : 9780080960135 |
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Genre | : Mathematics |
Author | : Aleksandr Sergeevich Kleshchëv |
Publisher | : American Mathematical Soc. |
Release | : 2012 |
File | : 148 Pages |
ISBN-13 | : 9780821874318 |
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.
Genre | : Mathematics |
Author | : Benjamin Steinberg |
Publisher | : Springer Science & Business Media |
Release | : 2011-10-23 |
File | : 166 Pages |
ISBN-13 | : 9781461407768 |