Affiliation: University of Miami
Email: morsej@math.miami.edu
Title Of Talk: Facts and figures about k-Schur functions
Abstract: The k-Schur functions arose in our study of an open problem on Macdonald polynomials. These symmetric functions provoked a k-refinement of classical ideas in symmetric function theory such as Pieri rules, Kostka numbers, the Young lattice, and Young tableaux. For example, the chains in the k-Young lattice are induced by the Pieri rules experimentally satisfied by k-Schur functions. We show that the k-Young lattice is isomorphic to the weak order on minimal coset representatives of the affine symmetric group modulo a maximal parabolic subgroup. Consequently, a bijection between k-tableaux and reduced words for these coset representatives naturally arises. We will also discuss how our work suggests that coefficients for the Macdonald polynomials may be q,t-enumerated by reduced words for affine permutations. This is joint work with Luc Lapointe.
Last update made Thu Nov 11 14:46:59 EST 2004.
Please report problems to:
frank@math.ufl.edu