Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants

Details Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants

2010-10-08

arxiv.org/abs/1010.1606v1

Mathematics

Commutative Algebra

37 pages

Scientific paper

Let $k$ be an algebraically closed field of positive characteristic, $G$ a
reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $P$ be a
parabolic subgroup of $G$, and $U_P$ its unipotent radical. We prove that if
$S$=\textyen $Sym V$ has a good filtration, then the ring of invariants
$S^{U_P}$ is strongly $F$-regular.

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