2 00 8 Torus quotients of homogeneous spaces - minimal dimensional Schubert Varieties admitting semi - stable points

In this paper, for any simple, simply connected algebraic group G of type B n , C n or D n and for any maximal parabolic subgroup P of G, we describe all minimal dimensional Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. In this paper, we also describe, for any semi-simple simply connected algebraic group G and for any Borel subgroup B of G, all Coxeter elements τ for which the Schubert variety X(τ) admits a semistable point for the action of the torus T with respect to a non-trivial line bundle on G/B.