Generic Hecke algebra for Renner monoids

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.