Symplctic Schur Q-functions

Abstract. Schur Q-functions are a family of symmetric functions introduced by Schur in his study of projective representations of symmetric groups. They are obtained by putting t=-1 in the Hall-Littlewood functions associated to the root system of type A. (Schur functions are the t=0 specialization.) This talk concerns symplectic Schur Q-functions, which are obtained by putting t=-1 in the Hall-Littlewood functions associated to the root system of type C. We discuss several Pfaffian identities as well as a combinatorial description for them. Also we present some positivity conjectures.