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Let V be an zz-dimensional vector space over complex numbers C. Let W be the rnth tensor product of V. If T CHom^F, V), let ®m T € Hom^lf, W) be the mth tensor product of T. The homomorphism T —► ® T is a representation of the full linear group GL (C). If H is a subgroup of the symmetric group S and X a linear character on H, let VTM(G) be the subspace of W consisting of all tensors symmetric with respect to // and X. Then V^(H) is invariant under ®m T. Let K(T) be the restriction of ®m T to VTM(H). For zz large compared with m and for H transitive, we determine all cases when the representation T —* K'T) is irreducible.

A class of representations of the full linear group. II