Centralizers of maximal regular subgroups in simple Lie groups and   relative congruence classes of representations
  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. 
M. Larouche, F. W. Lemire, J. Patera
math-ph math.MP