Symmetry classes of tensors as group modules

Let V be a finite dimensional vector space over C, H a subgroup of Sm, λ an irreducible character of H, and Vλ(H) the symmetry class of tensors associated with H and λ. If the vector space V is a C[G]-module, where G is a finite group, then the corresponding symmetry class of tensors naturally becomes a C[G]-module. In this paper, we study Vλ(H) as a C[G]-module and then obtain the corresponding character. Finally we will obtain some interesting applications of the character of this C[G]-module to the character theory of finite groups and the theory of numbers.