Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials

Details Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials

2010-07-26

arxiv.org/abs/1007.4431v2

2010 J. Phys. A: Math. Theor. 43 495207

Mathematics

Representation Theory

28 pages, 7 figures, 8 tables

Scientific paper

10.1088/1751-8113/43/49/495207

Polynomials in this paper are defined starting from a compact semisimple Lie group. A known classification of maximal, semisimple subgroups of simple Lie groups is used to select the cases to be considered here. A general method is presented and all the cases of rank not greater then 3 are explicitly studied. We derive the polynomials of simple Lie groups B_3 and C_3 as they are not available elsewhere. The results point to far reaching Lie theoretical connections to the theory of multivariable orthogonal polynomials.

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