Branching of Representations to Symmetric Subgroups

Abstract

Let $\gg$ be the Lie algebra of a compact Lie group and let $\theta$ be any automorphism of $\gg$. Let $\gk$ denote the fixed point subalgebra ${\gg }^{\theta }$. In this paper we present LiE programs that, for any finite dimensional complex representation $\pi$ of $\gg$, give the explicit branching $π|_\gk$ of $\pi$ on $\gk$. Cases of special interest include the cases where $\theta$ has order 2 (corresponding to compact riemannian symmetric spaces $G/K$), where $\theta$ has order 3 (corresponding to compact nearly--kaehler homogeneous spaces $G/K$), where $\theta$ has order 5 (which include the fascinating 5--symmetric space $E_8/A_4{A}_4$), and the cases where $\gk$ is the centralizer of a toral subalgebra of $\gg$.

28 pages, with a number of LiE programs for branching of representations to subgroups defined by automorphism, while keeping track of the action on both the center and the semisimple part of the subgroup

References in corpus (2)

• Graph inverse semigroups, groupoids and their C*-algebras
• Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint