Characters and inversions in the symmetric group

Characters and inversions in the symmetric group. (with A. de Medicis and M. Shimozono)
ABSTRACT: We consider sums over permutations in the symmetric group of the value of a skew character times q^inversions. Our main result gives a lower bound on the number of factors of 1+q and 1-q which divide the sum, and is shown to be sharp when the skew shape is a hook shape.
(This appeared as an extended abstract in the proceedings of the 6th Formal Power Series and Algebraic Combinatorics conference, at DIMACS in May 1994.)