TY - JOUR
T1 - Good filtrations of symmetric algebras and strong F-regularity of invariant subrings
AU - Hashimoto, Mitsuyasu
PY - 2001/3
Y1 - 2001/3
N2 - 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.
AB - 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.
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U2 - 10.1007/PL00004844
DO - 10.1007/PL00004844
M3 - Article
AN - SCOPUS:0035634444
SN - 0025-5874
VL - 236
SP - 605
EP - 623
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -