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| Author | : Aleksandr Sergeevich Kleshchëv |
| Publisher | : |
| Total Pages | : 292 |
| Release | : 2005 |
| Genre | : Hecke algebras |
| ISBN | : 9781107471641 |
| Author | : Alexander Kleshchev |
| Publisher | : Cambridge University Press |
| Total Pages | : 293 |
| Release | : 2005-06-30 |
| Genre | : Mathematics |
| ISBN | : 1139444069 |
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
| Author | : Peter Norman Hoffman |
| Publisher | : Oxford University Press |
| Total Pages | : 322 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780198535560 |
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.
| Author | : Gregory Karpilovsky |
| Publisher | : |
| Total Pages | : 672 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Pierre-Loic Meliot |
| Publisher | : CRC Press |
| Total Pages | : 666 |
| Release | : 2017-05-12 |
| Genre | : Mathematics |
| ISBN | : 1498719139 |
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.
| Author | : Peter Webb |
| Publisher | : Cambridge University Press |
| Total Pages | : 339 |
| Release | : 2016-08-19 |
| Genre | : Mathematics |
| ISBN | : 1107162394 |
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.
| Author | : Pavel I. Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853511 |
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.
| Author | : Alexei Borodin |
| Publisher | : Cambridge University Press |
| Total Pages | : 169 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107175550 |
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
| Author | : David A. Craven |
| Publisher | : Springer Nature |
| Total Pages | : 294 |
| Release | : 2019-08-30 |
| Genre | : Mathematics |
| ISBN | : 3030217922 |
This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.
| Author | : Roe Goodman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 731 |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 0387798528 |
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.
