Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs

Abstract

We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang Wang and the author. This is further applied to formulate and establish for the first time the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of the ortho-symplectic Lie superalgebra $\mathfrak{osp}(2m|2n)$.

Final version. Minor changes from version 1. arXiv admin note: text overlap with arXiv:1310.0103

Cited by in corpus (5)

• Canonical bases arising from quantum symmetric pairs of Kac-Moody type
• Canonical bases arising from quantum symmetric pairs
• Projective modules over classical Lie algebras of infinite rank in the parabolic category
• Multiparameter quantum Schur duality of type B
• Canonical bases arising from $ı$quantum covering groups