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We show that Hecke algebra of type B and a coideal subalgebra of the type Aquantum group satisfy a double centralizer property, generalizing theSchur-Jimbo duality in type A. The quantum group of type A and its coidealsubalgebra form a quantum symmetric pair. A new theory of canonical basesarising from quantum symmetric pairs is initiated. It is then applied toformulate and establish for the first time a Kazhdan-Lusztig theory for the BGGcategory O of the ortho-symplectic Lie superalgebras $\mathfrak{osp}(2m+1|2n)$.In particular, our approach provides a new formulation of the Kazhdan-Lusztigtheory for Lie algebras of type B/C.

A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs