The Frobenius morphism in invariant theory II.

Let R be the homogeneous coordinate ring of the Grassmannian G = Gr (2 , n) defined over an algebraically closed field k of characteristic p ≥ max ⁡ { n − 2 , 3 }. In this paper we give a description of the decomposition of R , considered as graded R p r -module, for r ≥ 2. This is a companion paper to [16] , where the case r = 1 was treated, and taken together, our results imply that R has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators D k (R) is simple, that G has global finite F-representation type (GFFRT) and that R provides a noncommutative resolution for R p r . [ABSTRACT FROM AUTHOR]