Irreducible representations of the rational Cherednik algebra associated to the Coxeter groupH3

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 ) .