### Abstract

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.

Original language | English |
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Pages (from-to) | 173-201 |

Number of pages | 29 |

Journal | Journal of Algebra |

Volume | 515 |

DOIs | |

Publication status | Published - 2018 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory