In 2004, Reiner, Stanton and White noticed that to an action of a cyclic group on a finite set one can often attach a polynomial with nonnegative integer coefficients. This polynomial has the property that when it is evaluated at specific roots of unity, the result is the size of the fixed point set for an element of the group. I will introduce the notion of 'promotion' on Young tableaux and via representation theory and geometry show that the polynomial attached to this action is the Kostka-Foulkes polynomial.

This is joint work with Joel Kamnitzer