The efficient computation of Fourier transforms on semisimple algebras (Q1783700)

In the article the problem of the efficient computation of a Fourier transform on a finite-dimensional complex semisimple algebra is discussed. The authors present general approach to the construction of efficient algorithms for computing a Fourier transform on a semisimple algebra and give a general result (Theorem 4.5) to find efficient Fourier transforms on a finite dimensional semisimple algebra with special subalgebra structure. Particular results include highly efficient algorithms for the Brauer, Temperley-Lieb, and Birman-Murakami-Wenzl algebras. To obtain these results authors use a connection between Bratteli diagrams and the derived path algebra and construction of Gelfand-Tsetlin bases.