Mixed expansion formula for the rectangular Schur functions and the affine Lie algebra A_1^(1)

Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of "mixed" products of Schur's S- and Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A_1^{(1)}. A realization of the basic representation that is of ``D_2^{(2)}''-type plays the central role.Comment: 21page

Virasoro Action on Schur Q-function (Women in Mathematics)

Schur Q-function was introduced by Schur as a symmetric polynomial describing the irreducible index of the projective representation of a symmetric group. A formula for Schur Qfunctions is presented which describes the action of the Virasoro operators. For strict partition, we prove a formula for each LkQλ. and L_kQλ. (k ≥ 1), where Lk is the Virasoro operator. The present paper is a résumé of [1] and [2]