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

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

2007-07-23

arxiv.org/abs/0707.3316v3

J. Reine Angew. Math. 628 (2009), 169--194.

Mathematics

Representation Theory

Latex file. 21 pages Final published version which corrects a previous error in definition 2.4.

Scientific paper

10.1515/CRELLE.2009.022

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 $1\le r'\le r$, $1\le n'\le n$, $ p'\mid p$ and where the parameters Q' are contained in a single $(\epsilon,q)$-orbit and $\epsilon$ is a primitive p'th root of unity.

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