Abstract
Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $B$ be a Borel subgroup of $G$, and $U$ its unipotent radical. We prove that if $S = \mathrm{Sym} \: V$ has a good filtration, then $S^U$ is $F$-pure.
Citation
Mitsuyasu HASHIMOTO. "Good filtrations and F-purity of invariant subrings." J. Math. Soc. Japan 63 (3) 815 - 818, July, 2011. https://doi.org/10.2969/jmsj/06330815
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