THE CYCLOTOMIC BMW ALGEBRA ASSOCIATED WITH THE TWO STRING TYPE B BRAID GROUP

The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B-n(k), introduced by R. Haring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Iwahori-Hecke algebras of type A. In this article, we produce a basis of the two strand algebra B-2(k) and construct its left regular representation. In the process we obtain relations amongst the parameters which play an important role in the n strand case.