Generic Hecke algebra for Renner monoids

Abstract

To each Renner monoid R we associate a generic Hecke algebra H ( R ) over Z [ q ] which is a deformation of the monoid Z -algebra of R. If M is a finite reductive monoid with Borel subgroup B and associated Renner monoid R, then we obtain the associated Iwahori–Hecke algebra H ( M , B ) by specialising q in H ( R ) and tensoring by C over Z , as in the classical case of finite reductive groups.