The eigenvalues of four-dimensional rotations

Let X be an orthosymplectie Lie superalgebra of type B or D. The weight structure of the tensor product moduleW=? ^M V, of M-copies of the natural representation. V, of X is studied from a partition point of view. A combinatorial characterization of the dominant weights of W and the weights of W which are highest weights for the finite dimensional irreducible modules is given. This partition point of view allows us to prove that the dominant weights of W and the weights of W which are highest weights for the finite dimensional irreducible modules stabilize as the rank of X gets large.