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arXiv:1609.02634 [math.RT]AbstractReferencesReviewsResources

The efficient computation of Fourier transforms on semisimple algebras

David Maslen, Daniel N. Rockmore, Sarah Wolff

Published 2016-09-09Version 1

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.

Comments: 22 pages, 13 figures, 2 appendices. arXiv admin note: text overlap with arXiv:1512.02445
Categories: math.RT
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