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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, and Vladimir Shchigolev, Lomonosov Moscow State University, Russia

Memoirs of the American Mathematical Society
2012; 123 pp; softcover
Volume: 220
ISBN-10: 0-8218-7431-4
ISBN-13: 978-0-8218-7431-8
List Price: US$71
Individual Members: US$42.60
Institutional Members: US$56.80
Order Code: MEMO/220/1034
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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

  • Preliminaries
  • Lowering operators
  • Some polynomials
  • Raising coefficients
  • Combinatorics of signature sequences
  • Constructing \(U(n-1)\)-primitive vectors
  • Main results on \(U(n)\)
  • Main results on projective representations of symmetric groups
  • Bibliography
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