Linear and Projective Representations of Symmetric Groups
Author: Aleksandr Sergeevich Kleshchëv
Publisher:
Published: 2005
Total Pages: 292
ISBN-13: 9781107471641
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Linear and Projective Representations of Symmetric Groups
Author: Alexander Kleshchev
Publisher: Cambridge University Press
Published: 2005-06-30
Total Pages: 293
ISBN-13: 1139444069
DOWNLOAD EBOOK →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
Projective Representations of the Symmetric Groups
Author: Peter Norman Hoffman
Publisher: Oxford University Press
Published: 1992
Total Pages: 322
ISBN-13: 9780198535560
DOWNLOAD EBOOK →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.
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$
Author: Aleksandr Sergeevich Kleshchëv
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 123
ISBN-13: 0821874314
DOWNLOAD EBOOK →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.
Projective Representations of Finite Groups
Author: Gregory Karpilovsky
Publisher:
Published: 1985
Total Pages: 672
ISBN-13:
DOWNLOAD EBOOK →This book presents a systematic account of this topic, from the classical foundations established by Schur 80 years ago to current advances and developments in the field. This work focuses on general methods and builds theory solidly on the study of modules over twisted group algebras, and provides a wide range of skill-sharpening mathematical techniques applicable to this subject. Offers an understanding of projective representations of finite groups for algebraists, number theorists, mathematical researchers studying modern algebra, and theoretical physicists.
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q(n)
Author: Aleksandr Sergeevich Kleshchëv
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 148
ISBN-13: 0821892061
DOWNLOAD EBOOK →There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. This work connects the two approaches to obtain new branching results for projective representations of symmetric groups.
A Course in Finite Group Representation Theory
Author: Peter Webb
Publisher: Cambridge University Press
Published: 2016-08-19
Total Pages: 339
ISBN-13: 1107162394
DOWNLOAD EBOOK →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.
Representations of the Infinite Symmetric Group
Author: Alexei Borodin
Publisher: Cambridge University Press
Published: 2017
Total Pages: 169
ISBN-13: 1107175550
DOWNLOAD EBOOK →An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Introduction to Representation Theory
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 240
ISBN-13: 0821853511
DOWNLOAD EBOOK →Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Symmetry, Representations, and Invariants
Author: Roe Goodman
Publisher: Springer Science & Business Media
Published: 2009-07-30
Total Pages: 731
ISBN-13: 0387798528
DOWNLOAD EBOOK →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.
