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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

Arithmetic Operation Jordan Block General Linear Group Associate Legendre Function Invariant Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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