# The Computational Complexity to Evaluate Representations of General Linear Groups

@article{Brgisser2000TheCC, title={The Computational Complexity to Evaluate Representations of General Linear Groups}, author={Peter B{\"u}rgisser}, journal={SIAM J. Comput.}, year={2000}, volume={30}, pages={1010-1022} }

We describe a fast algorithm to evaluate irreducible matrix representations of complex general linear groups ${\rm GL}_{m}$ with respect to a symmetry adapted basis (Gelfand--Tsetlin basis). This is complemented 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 $O(\ell\log\ell)$ algorithm to evaluate all associated Legendre…

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