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

Research paper by M. Larouche, F. W. Lemire, J. Patera

Indexed on: 30 Sep '11Published on: 30 Sep '11Published in: Mathematical Physics



Abstract

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.