Interpolation analogues of Schur $Q$-functions

We introduce interpolation analogues of the 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 a skew shifted Young diagram. This paper is a continuation of the author's paper math.CO/0303169 and is a partial projective analogue of the paper q-alg/9605042 by A. Okounkov and G. Olshanski, and of the paper math.CO/0110077 by G. Olshanski, A. Regev, and A. Vershik.