University of Canterbury Christchurch, New Zealand
Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group, and they can be defined combinatorially in terms of shifted tableaux. In this talk we describe planar decompositions of shifted tableaux into strips and use the shapes of these strips to generate pfaffians and determinants that are equal to Schur Q-functions. As special cases we obtain the classical pfaffian associated with Schur Q-functions, a pfaffian for skew Q--functions due to Jozefiak and Pragacz, and a determinantal expression of Okada.
The method discussed here has also been used to derive a general determinantal identity for Schur functions. The Jacobi-Trudi identity and the Giambelli identity are both special cases of this general result.