## 摘要

We show that for any singular dominant integral weight λ of a complex semisimple Lie algebra g, the endomorphism algebra B of any projective-injective module of the parabolic BGG category O_{λ} ^{p} is a symmetric algebra (as conjectured by Khovanov) extending the results of Mazorchuk and Stroppel for the regular dominant integral weight. Moreover, the endomorphism algebra B is equipped with a homogeneous (non-degenerate) symmetrizing form. In the appendix, there is a short proof due to K. Coulembier and V. Mazorchuk showing that the endomorphism algebra B_{λ} ^{p} of the basic projective-injective module of O_{λ} ^{p} is a symmetric algebra.

原文 | English |
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頁（從 - 到） | 173-201 |

頁數 | 29 |

期刊 | Journal of Algebra |

卷 | 515 |

DOIs | |

出版狀態 | Published - 2018 12月 1 |

## All Science Journal Classification (ASJC) codes

- 代數與數理論