Tensor product representations for orthosymplectic Lie superalgebras

Abstract

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⊗k which commutes with the action of the orthosymplectic Lie superalgebra spo(V) and the orthosymplectic Lie color algebra spo(V, β). We use the Brauer algebra action to compute maximal vectors in V⊗k and to decompose V⊗k into a direct sum of submodules Tλ. We compute the characters of the modules Tλ, give a combinatorial description of these characters in terms of tableaux, and model the decomposition of V⊗k into the submodules Tλ with a Robinson-Schensted-Knuth-type insertion scheme. © 1998 Elsevier Scienc..