Iwahori Hecke Algebras And Their Representation Theory

Author : Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig
Publisher : Springer
Page : 114 pages
File Size : 42,5 Mb
Release : 2003-07-03
Category : Mathematics
ISBN : 9783540362050

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Iwahori-Hecke Algebras and their Representation Theory by Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig Pdf

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Author : Meinolf Geck,Nicolas Jacon
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 49,8 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9780857297167

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Representations of Hecke Algebras at Roots of Unity by Meinolf Geck,Nicolas Jacon Pdf

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 : Andrew Mathas
Publisher : American Mathematical Soc.
Page : 204 pages
File Size : 44,9 Mb
Release : 1999
Category : Representations of algebras
ISBN : 9780821819265

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Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group by Andrew Mathas Pdf

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 : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 2002
Category : Hecke algebras
ISBN : OCLC:686055013

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Iwahori-Hecke Algebras and Their Representation Theory by Anonim Pdf

Author : Maria Welleda Baldoni
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2002
Category : Electronic
ISBN : OCLC:722824657

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Iwahori-Hecke Algebras and Their Representation Theory by Maria Welleda Baldoni Pdf

Author : George Lusztig
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 52,8 Mb
Release : 2003
Category : Hecke algebras
ISBN : 9780821833568

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Hecke Algebras with Unequal Parameters by George Lusztig Pdf

Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.

Author : Meinolf Geck,Götz Pfeiffer
Publisher : Oxford University Press
Page : 478 pages
File Size : 53,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0198502508

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Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras by Meinolf Geck,Götz Pfeiffer Pdf

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 : Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig
Publisher : Springer
Page : 114 pages
File Size : 46,6 Mb
Release : 2002-12-19
Category : Mathematics
ISBN : 3540002243

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Iwahori-Hecke Algebras and their Representation Theory by Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig Pdf

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Author : Pierre-Loic Meliot
Publisher : CRC Press
Page : 666 pages
File Size : 54,8 Mb
Release : 2017-05-12
Category : Mathematics
ISBN : 9781498719131

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Representation Theory of Symmetric Groups by Pierre-Loic Meliot Pdf

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 : Anonim
Publisher : Cambridge University Press
Page : 180 pages
File Size : 45,8 Mb
Release : 2024-06-28
Category : Hecke algebras
ISBN : 0821861581

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Hecke algebras by Anonim Pdf

Author : Seok-Jin Kang,Symposium on Lie Algebras,Myung-Hwan Kim,Insok Lee
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 50,8 Mb
Release : 1996
Category : Lie algebras
ISBN : 9780821805121

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Lie Algebras and Their Representations by Seok-Jin Kang,Symposium on Lie Algebras,Myung-Hwan Kim,Insok Lee Pdf

Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.

Author : Pierre-Loic Meliot
Publisher : CRC Press
Page : 433 pages
File Size : 47,5 Mb
Release : 2017-05-12
Category : Mathematics
ISBN : 9781315353852

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Representation Theory of Symmetric Groups by Pierre-Loic Meliot Pdf

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 : Nanhua Xi
Publisher : Springer
Page : 147 pages
File Size : 45,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540486824

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Representations of Affine Hecke Algebras by Nanhua Xi Pdf

Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

Author : Maria Chlouveraki
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 52,9 Mb
Release : 2009-09-14
Category : Mathematics
ISBN : 9783642030635

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Blocks and Families for Cyclotomic Hecke Algebras by Maria Chlouveraki Pdf

The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.

Author : Stephen Berman
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 48,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837016

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Infinite-dimensional Aspects of Representation Theory and Applications by Stephen Berman Pdf

The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.