𝕊_nFFT𝔽_p

The original 𝕊_nFFT package is a Julia package designed to facilitate harmonic analysis on the symmetric group of order n, denoted 𝕊_n. 𝕊_nFFT can be downloaded here. The version 𝕊_nFFT𝔽_p is based on representations of 𝕊_n with values in a finite field 𝔽_p.

The two main differences between the packages are the following:

• Young seminormal representations instead of Young orthogonal representations
• Working with BigInt modulo p (p prime) instead of Float64

Out of the box, this 𝕊_nFFT𝔽_p version implements:

• Group operations and factorizations for 𝕊_n
• Functionality to set up 𝔽_p valued functions over 𝕊_n
• The fast Fourier transform
• The inverse fast Fourier transform
• The fast convolution product of functions over 𝕊_n
• The fast exponentiation for the convolution product over 𝕊_n