---
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 $\mathfrak{osp}(2m|2n)$.'
address: 'Department of Mathematics, University of Maryland, College Park, MD 20742'
author:
- Huanchen Bao
title: 'Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs'
---

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Introduction {#introduction .unnumbered}
============

The Kazhdan-Lusztig theory provides the solution to the problem of determining the irreducible characters in the BGG category $\mc{O}$ of semisimple Lie algebras ([@KL; @BB; @BK]). The theory was originally formulated in 