Branching of representations to symmetric subgroups
Given a Lie algebra \(\mathfrak g\) and its subalgebra \(\mathfrak k\), the branching problem studies the restriction of a representation of \(\mathfrak g\) to \(\mathfrak k\). This article focuses on the branching problem where \(\mathfrak g\) is the Lie algebra of a compact Lie group, and \(\mathfrak k\) is the fixed point set \({\mathfrak g}^\theta\) of an automorphism \(\theta\) on \(\mathfrak g\). It presents a computing program for this purpose, known as the LiE program, available at \url{http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/}.NEWLINENEWLINEIt uses the LiE program to work out several cases where \(\theta\) has order 2, 3 and 5, and also where \(\mathfrak k\) is the centralizer of a toral subalgebra of \(\mathfrak g\).
scientific article; zbMATH DE number 6032505