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Rock Blocks
W. Turner, University of Oxford, England

Memoirs of the American Mathematical Society
2009; 102 pp; softcover
Volume: 202
ISBN-10: 0-8218-4462-8
ISBN-13: 978-0-8218-4462-5
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/202/947
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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.

Table of Contents

  • Introduction
  • Highest weight categories, \(q\)-Schur algebras, Hecke algebras, and finite general linear groups
  • Blocks of \(q\)-Schur algebras, Hecke algebras, and finite general linear groups
  • Rock blocks of finite general linear groups and Hecke algebras, when \(w < l\)
  • Rock blocks of symmetric groups, and the Brauer morphism
  • Schur-Weyl duality inside Rock blocks of symmetric groups
  • Ringel duality inside Rock blocks of symmetric groups
  • James adjustment algebras for Rock blocks of symmetric groups
  • Doubles, Schur super-bialgebras, and Rock blocks of Hecke algebras
  • Power sums
  • Schiver doubles of type \(A_\infty\)
  • Bibliography
  • Index
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