Efficient computation of Fourier inversion for finite groups

Abstract

Let G be a finite group and let f' be a complex-valued function on G. If p is a matrix represen~ation of G (of dimension LIP)then the Fourier trarzsfiirnz o~~at p k defined to be the matrix .f( p) = X, c ~f(s)p(s). Let % be a complete set of inequivalent irreducible matrix representations of G. The Foaner trarzsfomr of f (with respect to %') is defined as the set of matrices {jl p)},, ~~. Recove~of ~from its Fourier transform may be accomplished via the Fourier inlerscon formula, f(s) = ~~dPtrace(f( P) P(S)-'). pe9