The University of Michigan Combinatorics Seminar


Abstract 

Symmetric functions called kSchur functions arose in our study
of an open problem on Macdonald polynomials. We will discuss properties
of these functions that led us to the refinement of classical ideas
in symmetric function theory such as Pieri rules, Kostka numbers,
the Young lattice, and Young tableaux. Further, we will show how
these functions enabled us to find a bijection between refined Young
tableaux and reduced words for affine permutations. We will finish
by indicating a possible connection between the coefficients in the
kSchur function expansion of Macdonald polynomials and the affine
symmetric group. All necessary background for this talk will be provided
in the pretalk. 