Schur \(Q\)-functions and spin characters of symmetric groups. I
The main theorem of this paper is a combinatorial formula for the spin character (or projective character) for the symmetric group \(\zeta^\lambda_\pi\). A simpler formula for the case when \(\lambda\) has two parts is also given. These formulae are stated in terms of objects called ``complete separations of the partition \(\pi\)'' corresponding with a composition. A complete separation of \(\pi\) is an ordered set-partition of the numbers in \(\pi\) such that the block sums are determined by the composition. The character formulas are proved using several identities for Schur \(Q\)-functions. In addition to the authors' proofs, Theorems 3.5 and 2.2 have appeared in Section 1 of an article by \textit{P. Pragacz} [Algebro-geometric applications of Schur \(S\)- and \(Q\)-polynomials, Topics in invariant theory (Paris 1989/1990), Lect. Notes Math. 1478, 130-191 (1991; Zbl 0783.14031)].
scientific article; zbMATH DE number 907659