A generalization of the Kostka-Foulkes polynomials

Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases. Conjecturally these polynomials coincide with the Poincare polynomials of isotypic components of certain graded GL(n)-modules supported in a nilpotent conjugacy class closure in gl(n).Comment: 37 page

On a bijection between Littlewood-Richardson fillings of conjugate shape

We present a new bijective proof of the equality between the number of Littlewood-Richardson fillings of a skew-shape [lambda]/[mu] of weight [nu], and those of the conjugate skew-shape [lambda]t/[mu]t, of conjugate weight [nu]t. The bijection is defined by means of a unique permutation [alpha][lambda]/[mu] associated to the skew-shape [lambda]/[mu]. Our arguments use only well-established properties of Schensted insertion, and make no reference to jeu de taquin.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30058/1/0000426.pd