q,t-Fuss-Catalan numbers for complex reflection groups

Details q,t-Fuss-Catalan numbers for complex reflection groups q,t-Fuss-Catalan numbers for complex reflection groups

2008-06-18

arxiv.org/abs/0806.2936v1

Mathematics

Combinatorics

12 pages, 3 figures, to appear in DMTCS as part of the FPSAC 2008 conference proceedings

Scientific paper

In type A, the q,t-Fuss -Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group S_n. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and combinatorial properties of these polynomials in q and t. Finally, we present an idea how these polynomials could be related to some graded Hilbert series of modules arising in the context of rational Cherednik algebras. This is work in progress.

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