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 Plücker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety T ⑊ (X w v) T s s (ℒ) to be smooth. [ABSTRACT FROM AUTHOR]