Algebraic Families of Groups and Commuting Involutions

Abstract

Let $G$ be a complex affine algebraic group, and let ${\sigma }_1$ and ${\sigma }_2$ be commuting anti-holomorphic involutions of $G$. We construct an algebraic family of algebraic groups over the complex projective line and a real structure on the family that interpolates between the real forms $G^{{\sigma }_1}$ and $G^{{\sigma }_2}$.

References in corpus (3)

• Schwartz functions on Nash manifolds
• On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection
• Stacks in Representation Theory. What is a continuous representation of an algebraic group ?

Cited by in corpus (4)

• On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations
• Symmetries of the hydrogen atom and algebraic families
• Families of twisted $\mathcal{D}$-modules and arithmetic models of Harish-Chandra modules
• Families of Symmetries and the Hydrogen Atom