Abstract

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 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.

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