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Rock Blocks
 
W. Turner University of Oxford, Oxford, England
Front Cover for Rock Blocks
Available Formats:
Electronic 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
Front Cover for Rock Blocks
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  • Front Cover for Rock Blocks
  • Back Cover for Rock Blocks
Rock Blocks
W. Turner University of Oxford, Oxford, England
Available Formats:
Electronic 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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2022009; 102 pp
    MSC: 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.

  • 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 $
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Volume: 2022009; 102 pp
MSC: 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.

  • 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 $
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