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

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).Comment: Version 2: a minor error in 5.1 and its consequences in 3.1. and 3.2 corrected. Comments welcom