On the algebraic decomposition of a centralizer algebra of the hyperoctahedral group

In this paper we give a combinatorial rule for the decomposition of tenser powers of the signed permutation representation of the hyperoctahedral group. We then use this rule to describe the Bratteli diagram of a centralizer algebra of this group over k-th tenser space. We show that a basis for this algebra can be described completely in terms of set partitions and we give a set of generators and relations.