Satellites of spherical subgroups

Abstract

Let $G$ be a complex connected reductive algebraic group. Given a spherical subgroup $H\subset G$ and a subset $I$ of the set of spherical roots of $G/H$, we define, up to conjugation, a spherical subgroup $H_I\subset G$ of the same dimension of $H$, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincaré polynomials of the two spherical homogeneous spaces $G/H$ and $G/H_I$.

27 pages in English. Several minor changes and significantly improved exhibition. Main results unchanged. Accepted for publication in Algebraic Geometry journal

References in corpus (2)

• Wonderful Varieties: A geometrical realization
• Normalizers of solvable spherical subgroups

Cited by in corpus (1)

• Degenerations of spherical subalgebras and spherical roots