Visible actions on flag varieties of type C and a generalization of the Cartan decomposition
Let \(G\) be a connected compact simple Lie group of type \(C\), \(K\) a Chevalley-Weyl involution-fixed point subgroup and \(L,H\) Levi subgroups. The goal of present paper is to classify all the pairs \((L,H)\) such that \(G=LKH\). It is proved that this last relation holds if and only if 1) \((G,H)\) and \((G,L)\) are both symmetric pairs, or 2) \(L\) is a Levi subgroup of maximal dimension and \(H\) is an arbitrary maximal Levi subgroup up to switch of \(L,H\). An application to multiplicity-free theorems of representations is also discussed.
scientific article; zbMATH DE number 6214260
scientific article