The Multiplicity Of The Cell Modules Of The BMW Algebra In (V^?)_λ

Let m be a positive integer and let q be an indeterminate. In this paper, we denote by V the natural representation of quantum group Uq(sp2m) over the field C(q). Then the rth tensor product V(?)r is a left Uq(sp2m)-module. On the other hand, Wenzl [10] proved that V(?)r is a right Br(q,2m)-module where Br(q,2m) is the Birman-Murakami-Wenzl algebra with some special parameters. Further, Wenzl proved that V(?)r is the (Uq(sp2m),Br(q,2m))-bimodule. In particular, any weight space of V(?)r is a right Br(q,2m)-module.In this paper, we consider the case when m=3 and r=5. We will prove that a special weight space of V(?)5 has a filtration of cell modules for Br(q,6). Such a result is helpful for us to understand the structure of weight spaces of V(?)r in general.