Spherical homogeneous spaces of minimal rank N Ressayre

Spherical homogeneous spaces of minimal rank N. Ressayre Abstract. Let G be a complex connected reductive algebraic group and G/B denote the flag variety of G. A G-homogeneous space G/H is said to be spherical if H has a finite number of 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 proterties. 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. 1 Introduction Let G be a complex connected reductive algebraic group. Let B denote the flag variety of G. Let H be an algebraic subgroup of G which has a finite number of orbits in B ; the subgroup H and the homogeneous space G/H are said to be spherical. In this article, we study and classify a class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group G viewed as a G?G-homogeneous space. Namely, the pair (G,H) is called a spherical pair of minimal rank if there exists x in B such that the orbit H.

• ?? s?


• let h0


• introduction let


• s? fixes


• rank property


• such


• minimal rank


• g?g-homogeneous space


• knop also defined


• knop has