The University of Michigan Combinatorics Seminar
Fall 2002
October 11, 4:10-5:00, 3866 East Hall





The positivity of Kostka-Foulkes polynomials

Bogdan Ion

University of Michigan




Abstract

Described in the simplest terms the Kostka-Foulkes polynomials are the entries of the transition matrix from Hall-Littlewood 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 Kostka-Foulkes polynomials in terms of the charge statistic of semi-standard 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 Kac-Moody algebras.