Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computation of character decompositions of class functions on compact semisimple Lie groups

Authors: R. V. Moody and J. Patera
Journal: Math. Comp. 48 (1987), 799-827
MSC: Primary 22E46
MathSciNet review: 878707
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new algorithm is described for splitting class functions of an arbitrary semisimple compact Lie group K into sums of irreducible characters. The method is based on the use of elements of finite order (EFO) in K and is applicable to a number of problems, including decompositions of tensor products and various symmetry classes of tensors, as well as branching rules in group-subgroup reductions. The main feature is the construction of a decomposition matrix D, computed once and for all for a given range of problems and for a given K, which then reduces any particular splitting to a simple matrix multiplication. Determination of D requires selection of a suitable set S of conjugacy classes of EFO representing a finite subgroup of a maximal torus T of K and the evaluation of (Weyl group) orbit sums on S. In fact, the evaluation of D can be coupled with the evaluation of the orbit sums in such a way as to greatly enhance the efficiency of the latter. The use of the method is illustrated by some extensive examples of tensor product decompositions in $ {E_6}$. Modular arithmetic allows all computations to be performed exactly.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 22E46

Retrieve articles in all journals with MSC: 22E46

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society