### 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.

Original language | English |
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Pages (from-to) | 605-623 |

Number of pages | 19 |

Journal | Mathematische Zeitschrift |

Volume | 236 |

Issue number | 3 |

Publication status | Published - Mar 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Zeitschrift*,

*236*(3), 605-623.

**Good filtrations of symmetric algebras and strong F-regularity of invariant subrings.** / Hashimoto, Mitsuyasu.

Research output: Contribution to journal › Article

*Mathematische Zeitschrift*, vol. 236, no. 3, pp. 605-623.

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0035634444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035634444&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035634444

VL - 236

SP - 605

EP - 623

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3

ER -