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Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category

Monday, January 1st, 2018, 9:30 AM  华东师范大学

We show that for any singular dominant integral weight $\lambda$ of a complex semisimple Lie algebra $\mathfrak{g}$, the endomorphism algebra
$B_\lambda ^{\mathfrak{p}}$ of any projective-injective module in the parabolic BGG category $\mathcal{O}_\lambda^{\mathfrak{p}}$ 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 of any projective-injective module in $\mathcal{O}_\lambda^{\mathfrak{p}}$ equips with a homogeneous non-degenerate symmetrizing form. This is a joint work with Ngau Lam.

主持人:舒斌 教授

主办单位:数学系 科技处
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