On The Number of Classes of a Finite Group Invariant for Certain Substitutions

Abstract

In this paper we consider representations of groups over the field of the complex numbers.The nth-Kronecker power σ⊗n of an irreducible representation σ of a group can be decomposed into the constituents of definite symmetry with respect to the symmetric group Sn. In the special case of the general linear group GL(N) in N dimensions the decomposition of the defining representation at once provides irreducible representations of GL(N) [9; 10; 11].