Fast Evaluation of Representations of General Linear Groups
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 .
KeywordsArithmetic Operation Jordan Block General Linear Group Associate Legendre Function Invariant Matrix
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