Satake diagrams and real structures on spherical varieties

Abstract

With each antiholomorphic involution $\sigma$ of a connected complex semisimple Lie group $G$ we associate an automorphism ${\epsilon }_{\sigma }$ of the Dynkin diagram. The definition of ${\epsilon }_{\sigma }$ is given in terms of the Satake diagram of $\sigma$. Let $H\subset G$ be a self-normalizing spherical subgroup. If ${\epsilon }_{\sigma }=\mathrm{id}$ then we prove the uniqueness and existence of a $\sigma$-equivariant real structure on $G/H$ and on the wonderful completion of $G/H$.

V.3 - several typos corrected, some references changed

Cited by in corpus (7)

• Equivariant models of spherical varieties
• Real structures on horospherical varieties
• Spherical varieties over large fields
• Existence of equivariant models of G-varieties
• Real structures on symmetric spaces
• Existence of equivariant models of spherical varieties and other G-varieties
• Antiholomorphic involutions and spherical subgroups of reductive groups