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 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 - 1 Dec 2018 |
Keywords
- Parabolic BGG category
- Projective-injective modules
- Socular weights