Kazhdan Lusztig Cells With Unequal Parameters
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Kazhdan Lusztig Cells With Unequal Parameters
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Author : Cédric Bonnafé
language : en
Publisher: Springer
Release Date : 2018-05-07
Kazhdan Lusztig Cells With Unequal Parameters written by Cédric Bonnafé and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-07 with Mathematics categories.
This monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case. Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal work on the subject was published in 2002. The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group. Kazhdan-Lusztig Cells with Unequal Parameters will appeal to graduate students and researchers interested in related subject areas, such as Lie theory, representation theory, and combinatorics of Coxeter groups. Useful examples and various exercises make this book suitable for self-study and use alongside lecture courses. Information for readers: The character {\mathbb{Z}} has been corrupted in the print edition of this book and appears incorrectly with a diagonal line running through the symbol.
Kazhdan Lusztig Cells In Affine Weyl Groups With Unequal Parameters
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Author : Jérémie Guilhot
language : en
Publisher:
Release Date : 2008
Kazhdan Lusztig Cells In Affine Weyl Groups With Unequal Parameters written by Jérémie Guilhot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Hecke algebras categories.
Hecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.
Kazhdan Lusztig Cells In Type Bn With Unequal Parameters
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Author : Edmund Howse
language : en
Publisher:
Release Date : 2016
Kazhdan Lusztig Cells In Type Bn With Unequal Parameters written by Edmund Howse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Representation Theory Of Algebraic Groups And Quantum Groups
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Author : Akihiko Gyoja
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25
Representation Theory Of Algebraic Groups And Quantum Groups written by Akihiko Gyoja 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 2010-11-25 with Mathematics categories.
Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
Representations Of Hecke Algebras At Roots Of Unity
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Author : Meinolf Geck
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-18
Representations Of Hecke Algebras At Roots Of Unity written by Meinolf Geck 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 2011-05-18 with Mathematics categories.
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.
Group Representation Theory
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Author : Meinolf Geck
language : en
Publisher: EPFL Press
Release Date : 2007-05-07
Group Representation Theory written by Meinolf Geck and has been published by EPFL Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-07 with Mathematics categories.
After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).
Proceedings Of The International Conference On Complex Geometry And Related Fields
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Author : Zhijie Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Proceedings Of The International Conference On Complex Geometry And Related Fields written by Zhijie Chen 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 2007 with Mathematics categories.
In commemoration and celebration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields recently convened. This collection presents some of the conference highlights, dealing with various and significant topics of differential and algebraic geometry, while exploring their connections to number theory and mathematical physics. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Representations Of Reductive Groups
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Author : Monica Nevins
language : en
Publisher: Birkhäuser
Release Date : 2015-12-18
Representations Of Reductive Groups written by Monica Nevins and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-18 with Mathematics categories.
Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson
Characters Of Finite Coxeter Groups And Iwahori Hecke Algebras
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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2000
Characters Of Finite Coxeter Groups And Iwahori Hecke Algebras written by Meinolf Geck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
'An important book... The authors make full use of recent advances... The book is both a valuable resource for the expert and good starting point for the beginning researcher in this field... this is a very fine book which belongs on the shelves of anyone who is interested in the representation theory of Coxeter groups, Iwahori-Hecke algebras and, more generally, the groups of Lie type.' -Zentralblatt MATH'What makes the book especially valuable are the facts that the authors develop the various necessary theories nearly from the scratch... and that they include the algorithmic theory as well.' -Monatshefte för Mathematick'Written in an engaging and intelligible style... well structured and clearly printed.' -EMS'It will be a valuable reference for many years to come.' -Bulletin of the LMSFinite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, Lie algebras or theory of knots and links. This is the first book which develops the character theory of finite Coxeter groups and Iwahori-Hecke algebras in a systematic way, ranging from classical results to recent developments.
Commutative Algebra And Noncommutative Algebraic Geometry
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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-19
Commutative Algebra And Noncommutative Algebraic Geometry written by David Eisenbud 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 2015-11-19 with Mathematics categories.
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.