The Efficient Computation of Fourier Transforms on Semisimple Algebras



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, and Birman–Murakami–Wenzl algebras.


Fast Fourier transform Bratteli diagram Path algebra Quiver 

Mathematics Subject Classification

65250 43A30 05E40 20C15 



Daniel N. Rockmore was partially supported by AFOSR Award FA9550-11-1-0166 and the Neukom Institute for Computational Science at Dartmouth College. Sarah Wolff was partially supported by an NSF Graduate Fellowship.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • David Maslen
    • 1
  • Daniel N. Rockmore
    • 2
  • Sarah Wolff
    • 3
  1. 1.HBK Capital ManagementNew YorkUSA
  2. 2.Department of Mathematics and Computer ScienceDartmouth CollegeHanoverUSA
  3. 3.Department of Mathematics and Computer ScienceDenison UniversityGranvilleUSA

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