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The computational complexity to evaluate representations of general linear groups
Citation key B-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 $O(l\cdotłog(l))$ 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.
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