Generically Transitive Actions on Multiple Flag Varieties

Abstract

Let G be a semisimple algebraic group whose decomposition into a product of simple components does not contain simple groups of type A, and P ⊆ G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

Finite type multiple flag varieties of exceptional groups

“…Infinitely many orbits. The triple B 3 case and the triple C 3 case are shown to have infinitely many orbits in [4]. This leaves 8 more triples to check.…”

“…. = P k = P has been studied by Popov [9] and Devyatov [4], where they also consider the question when a variety (G/P ) k has an open orbit under the diagonal action of G.…”