This suite of modules is intended to implement the Fast Fourier Transform on arbitrarily large symmetric groups. The generalized FFT is a representation theoretic reinterpretation of the Discrete Fourier Transform. In particular, the classical FFT is the special case in which the function to be transformed is a function on the cyclic group of order n, where n denotes the number of data points. In fact, the Fourier coefficients are precisely the one dimensional representations of this group, namely the nth roots of unity.

This project is very much in preliminary stages. At this point, the code will implement a number of classical groups. Calculate dimensions of representations of the symmetric group, and construct its representations in matrix form.