Iwahori Hecke Algebras And Schur Algebras Of The Symmetric Group PDF Download
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Author | : Andrew Mathas |
Publisher | : American Mathematical Soc. |
Total Pages | : 204 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819267 |
Download Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group Book in PDF, ePub and Kindle
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.
Author | : Andrew Mathas |
Publisher | : |
Total Pages | : 73 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Hecke Algebras and Schur Algebras of the Symmetric Group Book in PDF, ePub and Kindle
Author | : Stuart Martin |
Publisher | : Cambridge University Press |
Total Pages | : 256 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 0521415918 |
Download Schur Algebras and Representation Theory Book in PDF, ePub and Kindle
The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory.
Author | : Pierre-Loic Meliot |
Publisher | : CRC Press |
Total Pages | : 433 |
Release | : 2017-05-12 |
Genre | : Mathematics |
ISBN | : 1315353857 |
Download Representation Theory of Symmetric Groups Book in PDF, ePub and Kindle
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 | : Zhaobing Fan |
Publisher | : American Mathematical Society |
Total Pages | : 108 |
Release | : 2023-01-18 |
Genre | : Mathematics |
ISBN | : 1470456265 |
Download Affine Hecke Algebras and Quantum Symmetric Pairs Book in PDF, ePub and Kindle
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Author | : Stephen Donkin |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 1998-12-10 |
Genre | : Mathematics |
ISBN | : 0521645581 |
Download The Q-Schur Algebra Book in PDF, ePub and Kindle
This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogs of certain results known already in the classical case. The approach is largely homological, based on Kempf's vanishing theorem for quantum groups and the quasi-hereditary structure of the q-Schur algebras. Beginning with an introductory chapter dealing with the relationship between the ordinary general linear groups and their quantum analogies, the text goes on to discuss the Schur Functor and the 0-Schur algebra. The next chapter considers Steinberg's tensor product and infinitesimal theory. Later sections of the book discuss tilting modules, the Ringel dual of the q-Schur algebra, Specht modules for Hecke algebras, and the global dimension of the q-Schur algebras. An appendix gives a self-contained account of the theory of quasi-hereditary algebras and their associated tilting modules. This volume will be primarily of interest to researchers in algebra and related topics in pure mathematics.
Author | : Meinolf Geck |
Publisher | : Springer Science & Business Media |
Total Pages | : 410 |
Release | : 2011-05-18 |
Genre | : Mathematics |
ISBN | : 0857297163 |
Download Representations of Hecke Algebras at Roots of Unity Book in PDF, ePub and Kindle
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
Author | : Meinolf Geck |
Publisher | : Oxford University Press |
Total Pages | : 478 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780198502500 |
Download Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras Book in PDF, ePub and Kindle
Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.
Author | : Wee Teck Gan |
Publisher | : World Scientific |
Total Pages | : 277 |
Release | : 2015-02-13 |
Genre | : Mathematics |
ISBN | : 9814651826 |
Download Modular Representation Theory Of Finite And P-adic Groups Book in PDF, ePub and Kindle
This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.
Author | : Klaus W. Roggenkamp |
Publisher | : Springer Science & Business Media |
Total Pages | : 488 |
Release | : 2001-08-31 |
Genre | : Mathematics |
ISBN | : 9780792371137 |
Download Algebra - Representation Theory Book in PDF, ePub and Kindle
Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.