Christian Stump - q,t-Fuß-Catalan numbers for complex reflection groups

dmtcs:3639 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3639
q,t-Fuß-Catalan numbers for complex reflection groupsConference paper

Authors: Christian Stump 1

  • 1 Faculty of Mathematics [Vienna]

In type A, the q,t-Fuß-Catalan numbers Cat(m)n(q,t) can be defined as a bigraded Hilbert series of a module associated to the symmetric group Sn. 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.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: qt-Catalan number,reflection group,Shi arrangement,coinvariant ring,rational Cherednik algebras,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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