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$q,t$-Fuß-Catalan numbers for complex reflection groups

Abstract : In type $A$, the $q,t$-Fuß-Catalan numbers $\mathrm{Cat}_n^{(m)}(q,t)$ can be defined as a bigraded Hilbert series of a module associated to the symmetric group $\mathcal{S}_n$. 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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Christian Stump. $q,t$-Fuß-Catalan numbers for complex reflection groups. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.295-306. ⟨hal-01185174⟩

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