Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H_3

TL;DR

This paper classifies and explicitly computes characters of all finite-dimensional irreducible representations in category O of the rational Cherednik algebra associated with the Coxeter group H_3 for any complex parameter.

Contribution

It provides a complete classification and character formulas for irreducible representations of the rational Cherednik algebra linked to H_3, a significant step in understanding these algebraic structures.

Findings

Explicit character formulas for all irreducible representations

Complete classification of finite-dimensional irreducible representations

Results valid for any complex parameter c

Abstract

This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute the characters of all these representations explicitly. As a consequence, we classify all the finite dimensional irreducible representations of H_c(H_3,h).