paper

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

arXiv:0707.3316 · doi:10.1515/CRELLE.2009.022

Abstract

We prove a Morita reduction theorem for the cyclotomic Hecke algebras H_{r,p,n}({q,Q}) $o f t y p e G (r, p, n) . A s a co n se q u e n ce, w es h o w t ha t co m p u t in g t h e d eco m p os i t i o nn u mb er so f H_{r, p, n} (Q) r e d u ces t oco m p u t in g t h e p^{'} - s pl i tt ab l e d eco m p os i t i o nn u mb er so f t h ecy c l o t o mi cH ec k e a l g e b r a s H_{r^{'}, p^{'}, n^{'}} (Q^{'}), w h er e$ 1\le r'\le r $,$ 1\le n'\le n $,$ p'\mid p $an d w h er e t h e p a r am e t er s Q^{'} a r eco n t ain e d ina s in g l e$ (Îµ,q) $- or bi t an d$ Îµ$ is a primitive p'th root of unity.

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