Schur Polynomials and Crystal Graphs

The Casselman-Shalika formula connects special values of p-adic Whittaker functions to characters of Schur polynomials in type A. We study the structure of the expansion of these Whittaker functions in order to derive new formulas for Schur polynomials. In particular, we give an algorithm for computing the necessary data in order to express the integrals that arise in the expansion. Furthermore, we completely compute all terms in a specific case for GL(4), which gives a new formula for Schur polynomials in four variables.