## Planar decompositions of shifted tableaux, pfaffians, and Schur Q-functions

**Angele Hamel **

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.