Spherical homogeneous spaces of minimal rank |
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Authors: | N. Ressayre |
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Affiliation: | Université Montpellier II, CC 51-Place Eugène Bataillon, 34095 Montpellier Cedex 5, France |
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Abstract: | Let G be a connected reductive algebraic group over an algebraically closed field K of characteristic zero. Let G/B denote the complete flag variety of G. A G-homogeneous space G/H is said to be spherical if H has finitely many orbits in G/B. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group G (viewed as a G×G-homogeneous space) has particularly nice properties. Namely, the pair (G,H) is called a spherical pair of minimal rank if there exists x in G/B such that the orbit H.x of x by H is open in G/B and the stabilizer Hx of x in H contains a maximal torus of H. In this article, we study and classify the spherical pairs of minimal rank. |
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Keywords: | Spherical varieties Schubert varieties and generalizations |
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