Tokuyama's Deformation of the Weyl Character Formula

In 1988, T. Tokuyama gave a surprising expression for Schur functions, in which a deformation parameter appears in both the numerator and denominator of the Weyl character formula, but not their quotient. We'll discuss various incarnations and generalizations of this formula, using both crystal bases and solvable lattice models from statistical mechanics. If time permits, we may discuss a third variant using an action on the weight ring by the affine Hecke algebra. These formulas arise naturally in matrix coefficients of p-adic representations, but this point of view will be minimized in the talk.

(This is joint work with Bump and Friedberg)