Journal of Fourier Analysis and Applications

, Volume 24, Issue 1, pp 226–284 | Cite as

Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

  • David Maslen
  • Daniel N. Rockmore
  • Sarah WolffEmail author


We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast Fourier Transform algorithms we make explicit use of the path algebra connection to the construction of Gel’fand–Tsetlin bases and work in the setting of quivers. We relate this framework to the construction of a configuration space derived from a Bratteli diagram. In this setting the complexity of an algorithm for computing a Fourier transform reduces to the calculation of the dimension of the associated configuration space. Our methods give improved upper bounds for computing the Fourier transform for the general linear groups over finite fields, the classical Weyl groups, and homogeneous spaces of finite groups, while also recovering the best known algorithms for the symmetric group.


Generalized Fourier transform Bratteli diagram Path algebra Computational complexity 

Mathematics Subject Classification

43A30 20C15 65T50 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

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

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