The efficient computation of Fourier transforms on semisimple algebras
Representation Theory
2016-09-12 v1
Abstract
We present a general diagrammatic approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra. This extends previous work wherein we derive best estimates for the computation of a Fourier transform for a large class of finite groups. We continue to find efficiencies by exploiting a connection between Bratteli diagrams and the derived path algebra and construction of Gel'fand-Tsetlin bases. Particular results include highly efficient algorithms for the Brauer, Temperley-Lieb algebras, and Birman-Murakami-Wenzl algebras.
Keywords
Cite
@article{arxiv.1609.02634,
title = {The efficient computation of Fourier transforms on semisimple algebras},
author = {David Maslen and Daniel N. Rockmore and Sarah Wolff},
journal= {arXiv preprint arXiv:1609.02634},
year = {2016}
}
Comments
22 pages, 13 figures, 2 appendices. arXiv admin note: text overlap with arXiv:1512.02445