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

2008/06/18 by Christian Stump, Stump, Christian
Mathematics · #05A15 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:20F55

paper · pdf · doi:10.48550/arxiv.0806.2936

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

arxiv created 2008/06/18 · arxiv updated 2009/12/01

Abstract

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.

Related

• q,t-Fuss-Catalan numbers for finite reflection groups
• Catalan numbers for complex reflection groups
• Rational Catalan Numbers for Complex Reflection Groups
• q-Schur algebras and complex reflection groups, I
• Invariants of polynomials mod Frobenius powers