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Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$
 
Alexander Kleshchev University of Oregon, Eugene, OR
Vladimir Shchigolev Lomonosov Moscow State University, Moscow, Russia
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$
eBook ISBN:  978-0-8218-9205-3
Product Code:  MEMO/220/1034.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$
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Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$
Alexander Kleshchev University of Oregon, Eugene, OR
Vladimir Shchigolev Lomonosov Moscow State University, Moscow, Russia
eBook ISBN:  978-0-8218-9205-3
Product Code:  MEMO/220/1034.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2202012; 123 pp
    MSC: Primary 20; Secondary 17;

    There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup \(Q(n)\) via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic \(p\) to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type \(A_{p-1}^{(2)}\).

    The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. Lowering operators
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2202012; 123 pp
MSC: Primary 20; Secondary 17;

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup \(Q(n)\) via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic \(p\) to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type \(A_{p-1}^{(2)}\).

The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. Lowering operators
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.