Double Kostka polynomials and Hall bimodule

Abstract

Double Kostka polynomials are polynomials indexed by a pair of double partitions. As in the ordinary case, double Kostka polynomials are defined in terms of Schur functions and Hall-Littlewood functions associated to double partitions. In this paper, we study combinatorial properties of those double Kostka polynomials and Hall-Littlewood functions. In particular, we show that the Lascoux-Schutzenberger type formula holds for double Kostka polynomials in certain cases. Moreover, we show that the Hall bimodule introduced by Finkelberg-Ginzburg-Travkin is isomorphic to the ring of symmetric functions with two types of variables, which gives an alternate approach for their result.

arXiv comment33 pages, including tables of double Kostka polynomials

Cited by in corpus (1)

• Fermionic formula for double Kostka polynomials