Algebraic families of groups and commuting involutions

Abstract

Let [Formula: see text] be a complex affine algebraic group, and let [Formula: see text] and [Formula: see text] be commuting anti-holomorphic involutions of [Formula: see text]. 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 [Formula: see text] and [Formula: see text].