Abstract:Let G be one of the ind-groups GL(∞), Ø(∞), Sp(∞), and P 1 , . . . , P ℓ be an arbitrary set of ℓ splitting parabolic subgroups of G. We determine all such sets with the property that G acts with finitely many orbits on the ind-variety X 1 × • • • × X ℓ where X i = G/P i . In the case of a finite-dimensional classical linear algebraic group G, the analogous problem has been solved in a sequence of papers of Littelmann, Magyar-Weyman-Zelevinsky and Matsuki. An essential difference from the finite-dimensional ca… Show more
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