Abstract
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 Z2-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.
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