| eBook ISBN: | 978-1-4704-0561-8 |
| Product Code: | MEMO/202/947.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
| eBook ISBN: | 978-1-4704-0561-8 |
| Product Code: | MEMO/202/947.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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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 non-describing 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.
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Table of Contents
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Chapters
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Introduction
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1. Highest weight categories, $q$-Schur algebras, Hecke algebras, and finite general linear groups
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2. Blocks of $q$-Schur algebras, Hecke algebras, and finite general linear groups
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3. Rock blocks of finite general linear groups and Hecke algebras, when $w<l$
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4. Rock blocks of symmetric groups, and the Brauer morphism
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5. Schur-Weyl duality inside Rock blocks of symmetric groups
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6. Ringel duality inside Rock blocks of symmetric groups
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7. James adjustment algebras for Rock blocks of symmetric groups
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8. Doubles, Schur super-bialgebras, and Rock blocks of Hecke algebras
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9. Power sums
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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 non-describing 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. Schur-Weyl 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 super-bialgebras, and Rock blocks of Hecke algebras
-
9. Power sums
-
10. Schiver doubles of type $A_\infty $
