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arXiv · 1109.6917

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

M. Larouche·F. W. Lemire·J. Patera
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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.

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M. Larouche, F. W. Lemire, J. Patera. 2011-09-30. Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations. https://doi.org/10.1088/1751-8113/44/41/415204

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