Catalan numbers for complex reflection groups

Details Catalan numbers for complex reflection groups Catalan numbers for complex reflection groups

2009-12-08

arxiv.org/abs/0912.1578v1

Mathematics

Combinatorics

9 pages

Scientific paper

We construct (q,t)-Catalan polynomials and q-Fuss-Catalan polynomials for any irreducible complex reflection group W. The two main ingredients in this construction are Rouquier's formulation of shift functors for the rational Cherednik algebras of W, and Opdam's analysis of permutations of the irreducible representations of W arising from the Knizhnik-Zamolodchikov connection.

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