Torus quotients of Richardson varieties

Abstract

Listen

Translate article

ABSTRACTIn this paper, for any simple, simply connected algebraic group G of type A and for any maximal parabolic subgroup P of G, we provide a criterion for a Richardson variety in G∕P to admit semistable points for the action of a maximal torus T with respect to an ample line bundle on G∕P. We study the structure of the Geometric invariant theory (GIT) quotient for the action of a maximal torus on the Richardson varieties in G2,n with respect to a suitable line bundle on G2,n. We also give a criterion for the Richardson varieties in to admit a semistable point with respect to the line bundle corresponding to the highest root.