Tensor product representations for orthosymplectic Lie superalgebras Original Research Article

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 Vcircle times operatork which commutes with the action of the orthosymplectic Lie superalgebra image(V) and the orthosymplectic Lie color algebra image(V, β). We use the Brauer algebra action to compute maximal vectors in Vcircle times operatork and to decompose Vcircle times operatork 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 Vcircle times operatork into the submodules Tλ with a Robinson-Schensted-Knuth-type insertion scheme.