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Catalan numbers for complex reflection groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 6, December 2012
- pp. 1491-1502
- 10.1353/ajm.2012.0047
- Article
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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.