Combinatorial expansions in K-theoretic bases

Abstract

We study the class C of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials, k-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of GLn, Grothendieck functions {Gλ} represent the K-theory of the same space. In this paper, we give a combinatorial description of the coefficients when any element of C is expanded in the G-basis or the basis dual to {Gλ}.