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

Jun Hu, Ngau Lam

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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 Oλ 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 Bλ p of the basic projective-injective module of Oλ p is a symmetric algebra.

Original languageEnglish
Pages (from-to)173-201
Number of pages29
JournalJournal of Algebra
Volume515
DOIs
Publication statusPublished - 2018 Dec 1

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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