Models of quasiprojective homogeneous spaces for Hopf algebras

Abstract

Given an affine group scheme G of finite type over a field k, a homogeneous space for G is a scheme X over k containing a rational point x such that G operates “transitively” on X . Assuming that G operates on the right, we may identify X with the quotient K\G of G by the left action of the stabilizer K of x in G. The representation-theoretic significance ofK\G is that the induction functor indK from K-modules to G-modules factors as a category equivalence