Astérisque N° 402/2018 - Grand Format

We show that Hecke algebra of type B and a coideal subal-gebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical hases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BCC category ß of the ortho-symplectic Lie superalgebras osp(2m + 1 ! 2n).
In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.