| Zusammenfassung |
We describe a fast algorithm to evaluate irreducible matrix representations of general linear groups $\mathrmGL(m,\mathbb C)$ 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 $O(l łog l)$ 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. |
