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

• Main Authors: Larouche, M, Lemire, F. W, Patera, J
• Format: Journal Article
• Language: English
• Published: 30-09-2011
• Subjects: Mathematics - Mathematical Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1109.6917

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