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}
}
  • Peter Bürgisser
  • Published 1 May 2000
  • Mathematics, Computer Science
  • SIAM J. Comput.
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… Expand
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