Catalan numbers for complex reflection groups

By I. Gordon, Stephen Griffeth. 2009

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We construct (q;t)-Catalan polynomials and q-Fuss-Catalan polynomials for any irreducible complex reection 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. In the special case of well-generated groups, this conrms conjectures of Bessis and Reiner.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/990f5305b38946e184e8db607de3e019f6ed56ca