Good filtrations of symmetric algebras and strong F-regularity of invariant subrings

Abstract

In this paper, we prove that a linear action of a reductive group on a polynomial ring with good filtrations over a field of characteristic p>0 yields a strongly F-regular (in particular, Cohen-Macaulay) invariant subring. The strongly F-regular property of some known examples of invariant subrings, such as the coordinate rings of Schubert varieties in Grassmannians, are recovered. A similar result over a field of characteristic zero is also proved.