A cellular basis of the q-Brauer algebra related with Murphy bases of Hecke algebras

Abstract

A new basis of the [Formula: see text]-Brauer algebra is introduced, which is a lift of Murphy bases of Hecke algebras of symmetric groups. This basis is shown to be a cellular basis in the sense of Graham and Lehrer. Using combinatorial tools we prove that the non-isomorphic simple [Formula: see text]-Brauer modules are indexed by the [Formula: see text]-restricted partitions of [Formula: see text] where [Formula: see text] is an integer, [Formula: see text]. When the [Formula: see text]-Brauer algebra has low dimension a criterion of semisimplicity is given, which is used to show that the [Formula: see text]-Brauer algebra is in general not isomorphic to the BMW-algebra.