The University of Michigan Combinatorics Seminar


Abstract 

Described in the simplest terms the KostkaFoulkes polynomials are the
entries of the transition matrix from HallLittlewood functions to Schur
functions. Foulkes conjectured in 1974 that they have positive
coefficients, fact which was not transparent from their definition, but
which later followed from alternative interpretations of the
KostkaFoulkes polynomials in terms of the charge statistic of
semistandard tableaux, cohomology of nilpotent orbits, and stalks at
unipotent classes of the general linear group over a finite field. I will
present a proof of the positivity based on their connection with the
Demazure characters of affine KacMoody algebras.
