The Representations Of Birman-Murakami-Wenzl Algebra B₈

Suppose k is a field which contains invertible elements r and q such that Char(k), the characteristic of k, is not equal to 2 and o(q2), the multiplicative order of q2, is strictly than 8. In this paper, we study the module structure of all cell modules of Birman-Murakami-Wenzl (or BMW) algebra (?)8 over the field k. Our results show that any cell module of (?)8 is multiplicity free except four possible cases.