Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

Details Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

2011-09-30

arxiv.org/abs/1109.6917v1

J. Phys. A: Math. Theor. 44 (2011) 415204

Physics

Mathematical Physics

27 pages

Scientific paper

10.1088/1751-8113/44/41/415204

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.

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