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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory