A CELLULAR BASIS OF THE q -BRAUER ALGEBRA RELATED WITH MURPHY BASES OF HECKE ALGEBRAS

A new basis of the q-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 q-Brauer modules are indexed by the e(q2)-restricted partitions of n − 2k where k is an integer, 0 ≤ k ≤ [n/2]. When the q-Brauer algebra has low dimension a criterion of semisimplicity is given, which is used to show that the q-Brauer algebra is in general not isomorphic to the BMW-algebra.