Equations Defining Symmetric Varieties and Affine Grassmannians

Suppose sigma be a simple involution of a semisimple algebraic group G, and suppose H is the subgroup of G of points fixed by sigma. If the restricted root system is of type A, C, or BC and G is simply connected, or if the restricted root system is of type B and G is of adjoint type, then we describe a standard monomial theory and the equations for the coordinate ring k[G/H] using the standard monomial theory and the Plucker relations of an appropriate (maybe infinite-dimensional) Grassmann variety.