Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q (Memoirs of the American Mathematical Society) - Softcover

Kleshchev, Alexander; Shchigolev, Vladimir

Softcover

ISBN 10: 0821874314 ISBN 13: 9780821874318

Publisher: Amer Mathematical Society, 2012

Synopsis

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 $Ap-1(2)$. 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.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2012
• Language: English
• ISBN 10: 0821874314
• ISBN 13: 9780821874318
• Binding: Paperback
• Number of pages: 123