PFAFFIANS AND DETERMINANTS FOR SCHUR Q-FUNCTIONS

Schur e-functions were originally introduced by Schur in relation to p rojective representations of the symmetric group, and they can be defi ned combinatorially in terms of shifted tableaux. In this paper we des cribe planar decompositions of shifted tableaux into strips and use th e shapes of these strips to generate pfaffians and determinants that a re equal to Schur e-functions. As special cases we obtain the classica l pfaffian associated with Schur e-functions, a pfaffian for skew e-fu nctions due to Jozefiak and Pragacz, and a determinantal expression of Okada. (C) 1996 Academic Press, Inc.