Electronic ISBN:  9781470405618 
Product Code:  MEMO/202/947.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 202; 2009; 102 ppMSC: Primary 20;
Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to \(q\)Schur algebras, or to finite general linear groups in nondescribing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.

Table of Contents

Chapters

Introduction

1. Highest weight categories, $q$Schur algebras, Hecke algebras, and finite general linear groups

2. Blocks of $q$Schur algebras, Hecke algebras, and finite general linear groups

3. Rock blocks of finite general linear groups and Hecke algebras, when $w<l$

4. Rock blocks of symmetric groups, and the Brauer morphism

5. SchurWeyl duality inside Rock blocks of symmetric groups

6. Ringel duality inside Rock blocks of symmetric groups

7. James adjustment algebras for Rock blocks of symmetric groups

8. Doubles, Schur superbialgebras, and Rock blocks of Hecke algebras

9. Power sums

10. Schiver doubles of type $A_\infty $


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Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to \(q\)Schur algebras, or to finite general linear groups in nondescribing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.

Chapters

Introduction

1. Highest weight categories, $q$Schur algebras, Hecke algebras, and finite general linear groups

2. Blocks of $q$Schur algebras, Hecke algebras, and finite general linear groups

3. Rock blocks of finite general linear groups and Hecke algebras, when $w<l$

4. Rock blocks of symmetric groups, and the Brauer morphism

5. SchurWeyl duality inside Rock blocks of symmetric groups

6. Ringel duality inside Rock blocks of symmetric groups

7. James adjustment algebras for Rock blocks of symmetric groups

8. Doubles, Schur superbialgebras, and Rock blocks of Hecke algebras

9. Power sums

10. Schiver doubles of type $A_\infty $