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Iwahori-Hecke algebras and Schur algebras of the symmetric group

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...

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Autor principal: Mathas, Andrew
Lenguaje:eng
Publicado: American Mathematical Society 1999
Materias:
Acceso en línea:http://cds.cern.ch/record/2623107
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author Mathas, Andrew
author_facet Mathas, Andrew
author_sort Mathas, Andrew
collection CERN
description 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.
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spelling cern-26231072021-04-21T18:47:37Zhttp://cds.cern.ch/record/2623107engMathas, AndrewIwahori-Hecke algebras and Schur algebras of the symmetric groupMathematical Physics and MathematicsThis 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.American Mathematical Societyoai:cds.cern.ch:26231071999
spellingShingle Mathematical Physics and Mathematics
Mathas, Andrew
Iwahori-Hecke algebras and Schur algebras of the symmetric group
title Iwahori-Hecke algebras and Schur algebras of the symmetric group
title_full Iwahori-Hecke algebras and Schur algebras of the symmetric group
title_fullStr Iwahori-Hecke algebras and Schur algebras of the symmetric group
title_full_unstemmed Iwahori-Hecke algebras and Schur algebras of the symmetric group
title_short Iwahori-Hecke algebras and Schur algebras of the symmetric group
title_sort iwahori-hecke algebras and schur algebras of the symmetric group
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2623107
work_keys_str_mv AT mathasandrew iwahoriheckealgebrasandschuralgebrasofthesymmetricgroup