Schur Q-functions and spin characters of symmetric groups I

In a classic paper, I. Schur [6] introduced a class of symmetric functions, now called Schur Qfunctions, in order to determine the irreducible spin (projective) characters of symmetric groups. In the case of the ordinary characters of symmetric groups, going back to the early work of D. E. Littlewood and A. R. Richardson [3], the corresponding Schur functions have been used to give useful combinatorial formulae for determining explicit values for these characters (see for example [2]). Our aim in this paper is to obtain combinatorial formulae for the spin characters. We see that as always in the spin case, the formulae are considerably more complicated with a number of new interesting phenomena arising.