Staircase Macdonald polynomials and the $q$-Discriminant

Details Staircase Macdonald polynomials and the $q$-Discriminant Staircase Macdonald polynomials and the $q$-Discriminant

2008-01-16

arxiv.org/abs/0801.2443v1

FPSAC 2008, Chili (2008)

Mathematics

Combinatorics

14 pp

Scientific paper

We prove that a $q$-deformation $\Disc k\X q$ of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of $\Disc k\X q$ on different basis of symmetric functions. In particular, we show that its expansion on the monomial basis can be explicitly described in terms of standard tableaux and we generalize a result of King-Toumazet-Wybourne about the expansion of the $q$-discriminant on the Schur basis.

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