Morita equivalences of the cyclotomic Hecke algebras of type G(r,p,n)

Jun Hu and Andrew Mathas

Abstract

We prove a Morita reduction theorem for the cyclotomic Hecke algebras H_r,p,n({q,Q}) of type G(r,p,n). As a consequence, we show that computing the decomposition numbers of H_r,p,n(Q) reduces to computing the p'-splittable decomposition numbers of the cyclotomic Hecke algebras H_r',p',n'(Q'), where 1≤ r'≤ r, 1≤ n'≤ n, p'| p and where the parameters Q' are contained in a single (ε,q)-orbit and ε is a primitive p'-th root of unity.

Keywords: Hecke algebras, complex reflection groups, representation theory.

AMS Subject Classification: Primary 20C08; secondary 20C30.