Elementary Divisors Of Induced Transformations On Symmetry Classes Of Tensors

Let Vχ(G) denote the symmetry class of tensors over the vector space V associated with the permutation group G and irreducible character χ. Write v1*v2*...*vm for the decomposable symmetrized product of the indicated vectors (m=degG). If T is a linear operator on V, let K(T) denote the associated operator on Vχ(G), i.e., K(T)v1*v2*...*vm=Tv1*Tv2*...*Tvm. Denote by D(T) the derivation operator D(T)v1*v2*...*vm=Tv1*v2...*vm+v1*Tv2*v3* ...*vm+...+v1*v2*...*vm–1*Tvm. The article concerns the elementary divisors of K(T) and D(T).