Memoirs of the American Mathematical Society 2012; 123 pp; softcover Volume: 220 ISBN10: 0821874314 ISBN13: 9780821874318 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/220/1034
 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 KacMoody algebra of type \(A_{p1}^{(2)}\). 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 \(U(n1)\)primitive vectors
 Main results on \(U(n)\)
 Main results on projective representations of symmetric groups
 Bibliography
