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• W2963482009 abstract "Let G be a reductive algebraic group over the complex number filed, and K = G^{theta} be the fixed points of an involutive automorphism theta of G so that (G, K) is a symmetric pair. We take parabolic subgroups P and Q of G and K respectively and consider a product of partial flag varieties G/P and K/Q with diagonal K-action. The double flag variety G/P times K/Q thus obtained is said to be of finite type if there are finitely many K-orbits on it. A triple flag variety G/P^1 times G/P^2 times G/P^3 is a special case of our double flag varieties, and there are many interesting works on the triple flag varieties. In this paper, we study double flag varieties G/P times K/Q of finite type. We give efficient criterion under which the double flag variety is of finite type. The finiteness of orbits is strongly related to spherical actions of G or K. For example, we show a partial flag variety G/P is K-spherical if a product of partial flag varieties G/P times G/theta(P) is G-spherical. We also give many examples of the double flag varieties of finite type, and for type AIII, we give a classification when P = B is a Borel subgroup of G." @default.
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• W2963482009 date "2011-01-10" @default.
• W2963482009 modified "2023-10-18" @default.
• W2963482009 title "Double flag varieties for a symmetric pair and finiteness of orbits" @default.
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