On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

Details On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

2005-01-25

arxiv.org/abs/math/0501446v1

Mathematics

Representation Theory

21 pages, 6 tables

Scientific paper

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P-hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there is a polynomial time algorithm, based on counting the lattice points in polytopes. In fact, for Lie algebras of type A_r, there is an algorithm, based on the ellipsoid algorithm, to decide when the coefficients are nonzero in polynomial time for arbitrary rank. Our experiments show that the lattice point algorithm is superior in practice to the standard techniques for computing multiplicities when the weights have large entries but small rank. Using an implementation of this algorithm, we provide experimental evidence for conjectured generalizations of the saturation property of Littlewood--Richardson coefficients. One of these conjectures seems to be valid for types B_n, C_n, and D_n.

Affiliated with

Also associated with

No associations

Rating

On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513658