Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H3

This paper describes irreducible representations in category O of the rational Cherednik algebra Hc(H3,h) associated to the exceptional Coxeter group H3 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 Hc(H3,h).