Hall-Littlewood vertex operators and generalized Kostka polynomials

A family of vertex operators that generalizes those given by Jing for the H all Littlewood symmetric functions is presented. These operators produce sy mmetric functions related to the Poincare polynomials referred to as genera lized Kostka polynomials in the same way that Jing's operator produces symm etric functions related to Kostka Foulkes polynomials. These operators are then used to derive commutation relations and new relations involving the g eneralized Kostka coefficients. Such relations may be interpreted as identi ties in the (GL(n) x C)- equivariant K-theory of the nulleone. (C) 2001 Aca demic Press.