We derive a general result about commuting actions on certain objects in braided rigid monoidal categories. This enables us to de ne 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; ). We use the Brauer algebra action to compute maximal vectors in V k and to decompose V k into a direct sum of submodules T . We compute the characters of the modules T , give a combinatorial description of these characters in terms of tableaux, and model the decomposition of V k into the submodules T with a Robinson-Schensted-Knuth type insertion scheme.

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