English

Catalan numbers for complex reflection groups

Combinatorics 2009-12-09 v1 Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.0912.1578,
  title  = {Catalan numbers for complex reflection groups},
  author = {Iain Gordon and Stephen Griffeth},
  journal= {arXiv preprint arXiv:0912.1578},
  year   = {2009}
}

Comments

9 pages

R2 v1 2026-06-21T14:21:17.597Z