Kronecker products of representations of the exceptional groups

Englefield, M. J.

doi:10.1016/0378-4371(82)90296-5

Physica A: Statistical Mechanics and its Applications

1982

DOI: 10.1016/0378-4371(82)90296-5

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Kronecker products of representations of the exceptional groups

M. J. Englefield

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1987

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“…There are other E6 tensor product decomposition tables in the literature [11], [26], [28], calculated by entirely different methods. We have made no attempt to compare these methods with the one here.…”

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confidence: 99%

Computation of Character Decompositions of Class Functions on Compact Semisimple Lie Groups

Moody¹,

Patera²

1987

Mathematics of Computation

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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 E6. Modular arithmetic allows all computations to be performed exactly.

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mentioning

confidence: 99%

Computation of Character Decompositions of Class Functions on Compact Semisimple Lie Groups

Moody¹,

Patera²

1987

Mathematics of Computation

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Kronecker products of representations of the exceptional groups

Cited by 1 publication

References 3 publications

Computation of Character Decompositions of Class Functions on Compact Semisimple Lie Groups

Computation of Character Decompositions of Class Functions on Compact Semisimple Lie Groups

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