Representations Of Hecke Algebras At Roots Of Unity
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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.
Representations Of Quantum Algebras And Combinatorics Of Young Tableaux
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Author : Susumu Ariki
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Representations Of Quantum Algebras And Combinatorics Of Young Tableaux written by Susumu Ariki 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 2002 with Mathematics categories.
This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Iwahori Hecke Algebras And Schur Algebras Of The Symmetric Group
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Author : Andrew Mathas
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Iwahori Hecke Algebras And Schur Algebras Of The Symmetric Group written by Andrew Mathas 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 1999 with Mathematics categories.
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.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date :
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab 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 with Mathematics categories.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
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 Algebraic Groups Quantum Groups And Lie Algebras
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Author : Georgia Benkart
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Representations Of Algebraic Groups Quantum Groups And Lie Algebras written by Georgia Benkart 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 2006 with Mathematics categories.
Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.
Infinite Dimensional Aspects Of Representation Theory And Applications
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Infinite Dimensional Aspects Of Representation Theory And Applications written by Stephen Berman 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 2005 with Mathematics categories.
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.
Symmetries Integrable Systems And Representations
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Author : Kenji Iohara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries Integrable Systems And Representations written by Kenji Iohara 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 2012-12-06 with Mathematics categories.
This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Geometric Analysis And Lie Theory In Mathematics And Physics
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Author : Alan L. Carey
language : en
Publisher: Cambridge University Press
Release Date : 1998
Geometric Analysis And Lie Theory In Mathematics And Physics written by Alan L. Carey 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 1998 with Mathematics categories.
Graduate lectures on the interface between mathematics and physics.
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).