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There are two approaches to projective representation theory of symmetric andalternating groups, which are powerful enough to work for modularrepresentations. One is based on Sergeev duality, which connects projectiverepresentation theory of the symmetric group and representation theory of thealgebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schurfunctors.  The second approach follows the work of Grojnowski for classical affine andcyclotomic Hecke algebras and connects projective representation theory ofsymmetric groups in characteristic $p$ to the crystal graph of the basic moduleof 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 toobtain new branching results for projective representations of symmetricgroups. This is achieved by developing the theory of lowering operators for thesupergroup $Q(n)$ which is parallel to (although much more intricate than) thesimilar theory for $GL(n)$ developed by the first author. The theory oflowering operators for $GL(n)$ is a non-trivial generalization of Carter's workin characteristic zero, and it has received a lot of attention. So this part ofour work might be of independent interest.  One of the applications of lowering operators is to tensor products ofirreducible $Q(n)$-modules with natural and dual natural modules, which leadsto important special translation functors. We describe the socles and primitivevectors in such tensor products.

Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)