Interpolation analogues of Schur Q-functions

Abstract

We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula for the transition coefficients between multiparameter Schur Q-functions with different parameters. We write an explicit Pfaffian expression for the dimension of skew shifted Young diagram. This paper is a continuation of author's paper math.CO/0303169 and is a partial projective analogue of the paper by A. Okounkov and G. Olshanski q-alg/9605042, and of the paper by G. Olshanski, A. Regev and A. Vershik math.CO/0110077.