Fast Evaluation of Representations of General Linear Groups

  • Peter Bürgisser
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 7)

Abstract

We describe a fast algorithm to evaluate irreducible rational matrix representations of complex general linear groups GL m with respect to a symmetry adapted basis (Gelfand-Tsetlin basis). We complement this by a lower bound, which shows that our algorithm is optimal up to a factor m 2 with regard to nonscalar complexity. Our algorithm can be used for the fast evaluation of special functions: for instance, we obtain an O(ℓlogℓ) algorithm to evaluate all associated Legendre functions of order ℓ. The results of this chapter are from Bürgisser [17].

Keywords

Hull Sine 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter Bürgisser
    • 1
  1. 1.Fachbereich 17 • Mathematik-InformatikUniversität-Gesamthochschule PaderbornPaderbornGermany

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