Spherical homogeneous spaces of minimal rank

Nicolas Ressayre (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group $G$ (viewed as a $G\times G$-homogeneous space) has particularly nice proterties. Namely, the pair $(G,H)$ is called a {\it 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 $H_x$ of $x$ in $H$ contains a maximal torus of $H$. In this article, we study and classify the spherical pairs of minimal rank.

Mots clés: Spherical homogeneous spaces

Domaines: Géométrie algébrique [math.AG]

Nicolas Ressayre. Spherical homogeneous spaces of minimal rank. Advances in Mathematics, 2010, 224 (5), pp.1784-1800. ⟨10.1016/j.aim.2010.01.014⟩. ⟨hal-00412655⟩