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.