The Frobenius morphism in invariant theory II

Abstract

Let R be the homogeneous coordinate ring of the Grassman-nian 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 Rpr-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 Dk(R) is simple, that G has global finite F-representation type (GFFRT) and that R provides a noncommutative resolution for Rpr . (c) 2022 Published by Elsevier Inc.