Let G be a connected reductive algebraic group over the field of
complex numbers C. Let Y=G/H be a spherical homogeneous space of G (a
homogeneous space of special kind). Let G_0 be a real model (real form) of G,
that is, a model of G over the field of real numbers R. In the talk I will
discuss the following question: does there exist a G_0 equivariant real
model Y_0 of Y? This is interesting even in the case when G = G' x G', where
G' is a connected semisimple group over C, and H=G' embedded diagonally into
G' x G'.
No preliminary knowledge of sperical varieties will be assumed.
