Tensor product representations for orthosymplectic Lie superalgebras

We derive a general result about commuting actions on certain objects in braided rigid monoidal categories. This enables us to define an action of the Brauer algebra on the tensor space V-xk which commutes with the action of the orthosymplectic Lie superalgebra spo(V) and the orthosymplectic Lie color algebra spo(V,beta). Pie use the Brauer algebra action to compute maximal vectors in V-xk and to decompose V-xk into a direct sum of submodules T-lambda. We compute the characters of the modules T-lambda, give a combinatorial description of these characters in terms of tableaux, and model the decomposition of V-xk into the submodules T-lambda with a Robinson-Schensted-Knuth-type insertion scheme. (C) 1998 Elsevier Science B.V, All rights reserved.