Smooth torus quotients of Richardson varieties in the Grassmannian

Let k and n be positive coprime integers with k < n. Let T denote the subgroup of diagonal matrices in SL(n, C). We study the GIT quotient of Richardson varieties X-w(v) in the Grassmannian Gr(k,n) by T with respect to a T-linearized line bundle L corresponding to the Plucker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety T\\(X-w(v))(T)(ss) (L) to be smooth.