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Rock blocks
About this Title
W. Turner
Publication: Memoirs of the American Mathematical Society
Publication Year:
2009; Volume 202, Number 947
ISBNs: 978-0-8218-4462-5 (print); 978-1-4704-0561-8 (online)
DOI: https://doi.org/10.1090/S0065-9266-09-00562-6
Published electronically: July 22, 2009
Keywords: Hog eye,
latchkey,
master,
opener,
passkey,
screw,
skeleton,
twister
MSC: Primary 20C30
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. 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 $A_\infty$
Abstract
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, we pursue a structure theorem for these blocks.- J. L. Alperin, Weights for finite groups, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 369–379. MR 933373, DOI 10.1090/pspum/047.1/933373
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