Z2-graded Clifford system in the Hecke algebra of type Bn

We extend the representation theory of the q-analogue of the alternating group to the Hecke algebra of type Bn. We show that the Hecke algebra of type Bn has a -graded Clifford system. Using this result, we introduce a new subalgebra in the Hecke algebra of type Bn. This subalgebra is an extension of the q-analogue of the alternating group. The branching rule for the Hecke algebra of type Bn is given by making use of the generalized Clifford theory.