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Given a complex representation of a finite group G , construct the integer valued function *e on G by setting (v(g) to be the dimension of the fixed-point-space of g in the module corresponding to the given representation. Usually, *e is not a generalized character of G and for trivial reasons G(in is always a generalized character. The main result of this paper is that ev is always a generalized character, where e is the exponent Qf G .

The fixed-point-space dimension function for a finite group representation