FFT on the symmetric group.
.NET Wrapper for the SnOB library. A C++ library for computing fast Fourier transforms on the symmetric group. SnOB can be found here: http://people.cs.uchicago.edu/~risi/SnOB/index.html
The work of Risi Kondor: http://people.cs.uchicago.edu/~risi/
Thesis: http://people.cs.uchicago.edu/~risi/papers/KondorThesis.pdf
Video Lectures: http://videolectures.net/risi_kondor/