ALTERNATING SIGN MATRICES AND SOME DEFORMATIONS OF WEYL DENOMINATOR FORMULAS

An alternating sign matrix is a square matrix whose entries are 1, 0, or - 1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products [GRAPHICS] as sums indexed by sets of alternating sign matrices invariant under a 180-degrees rotation. If we put t = 1 these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B(n) and C(n). A similar deformation of the denominator formula for type D(n) is also given.