Rock Blocks For Double Covers Of Symmetric Groups And Quiver Hecke Superalgebras
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Rock Blocks For Double Covers Of Symmetric Groups And Quiver Hecke Superalgebras
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Author : Alexander S. Kleshchev
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-16
Rock Blocks For Double Covers Of Symmetric Groups And Quiver Hecke Superalgebras written by Alexander S. Kleshchev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-16 with Mathematics categories.
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Diagrammatic Algebra
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Author : Chris Bowman
language : en
Publisher: Springer Nature
Release Date : 2025-05-02
Diagrammatic Algebra written by Chris Bowman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-02 with Mathematics categories.
Diagrammatic Algebra provides the intuition and tools necessary to address some of the key questions in modern representation theory, chief among them Lusztig’s conjecture. This book offers a largely self-contained introduction to diagrammatic algebra, culminating in an explicit and entirely diagrammatic treatment of Geordie Williamson’s explosive torsion counterexamples in full detail. The book begins with an overview of group theory and representation theory: first encountering Coxeter groups through their actions on puzzles, necklaces, and Platonic solids; then building up to non-semisimple representations of Temperley–Lieb and zig-zag algebras; and finally constructing simple representations of binary Schur algebras using the language of coloured Pascal triangles. Next, Kazhdan–Lusztig polynomials are introduced, with their study motivated by their combinatorial properties. The discussion then turns to diagrammatic Hecke categories and their associated p-Kazhdan–Lusztig polynomials, explored in a hands-on manner with numerous examples. The book concludes by showing that the problem of determining the prime divisors of Fibonacci numbers is a special case of the problem of calculating p-Kazhdan–Lusztig polynomials—using only elementary diagrammatic calculations and some manipulation of (5x5)-matrices. Richly illustrated and assuming only undergraduate-level linear algebra, this is a particularly accessible introduction to cutting-edge topics in representation theory. The elementary-yet-modern presentation will also be of interest to experts.
Representation Theory Of Finite Groups A Guidebook
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Author : David A. Craven
language : en
Publisher: Springer Nature
Release Date : 2019-08-30
Representation Theory Of Finite Groups A Guidebook written by David A. Craven and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.
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.
Rock Blocks
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Author : Will Turner
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-08
Rock Blocks written by Will Turner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to $q$-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.
Tensor Categories
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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05
Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
The Kepler Conjecture
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Author : Jeffrey C. Lagarias
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-09
The Kepler Conjecture written by Jeffrey C. Lagarias and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-09 with Mathematics categories.
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.
Linear And Projective Representations Of Symmetric Groups
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Author : Alexander Kleshchev
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-30
Linear And Projective Representations Of Symmetric Groups written by Alexander Kleshchev and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-30 with Mathematics categories.
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
Automorphisms Of Finite Groups
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Author : Inder Bir Singh Passi
language : en
Publisher: Springer
Release Date : 2019-01-12
Automorphisms Of Finite Groups written by Inder Bir Singh Passi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-12 with Mathematics categories.
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Combinatorial Convexity
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Author : Imre Bárány
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-04
Combinatorial Convexity written by Imre Bárány and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Education categories.
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.