q,t-Fuss-Catalan numbers for complex reflection groups
Abstract
Description
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.
12 pages, 3 figures, to appear in DMTCS as part of the FPSAC 2008 conference proceedings
12 pages, 3 figures, to appear in DMTCS as part of the FPSAC 2008 conference proceedings