@article{B-The-Computational-Complexity-To-Evaluate-Representations-Of-General-Linear-Groups,
Title = {The computational complexity to evaluate representations of general linear groups},
Author = {Peter Bürgisser},
Pages = {1010-1022},
Year = {2000},
Journal = {SIAM J. Comp.},
Volume = {30},
Number = {3},
Abstract = {We describe a fast algorithm to evaluate irreducible matrix representations of general linear groups $\mathrm G\mathrm L(m,\mathbb C)$ 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 $O(l\cdot\log(l))$ algorithm to evaluate all associated Legendre functions of degree $l$. As a further application we obtain an algorithm to evaluate immanants, which is faster than previous algorithms due to Hartmann and Barvinok.},
Url = {http://www3.math.tu-berlin.de/algebra/work/rev-gl-exab.pdf},
Url2 = {http://epubs.siam.org/doi/abs/10.1137/S0097539798367892}
}