Abstract: In Part II, we develop a new duality featuring Hecke algebra of type B, and use it to develop a new theory of canonical basis of quantum symmetric pairs, different from Lusztig's. This allows us to formulate and establish for the first time the KL conjecture of the ortho-symplectic Lie superalgebras; in particular, this provides a new reformulation of KL theory of classical Lie algebras. This is joint work with Huanchen Bao (Virginia).

Abstract of Part I