A NEW APPROACH TO KAZHDAN-LUSZTIG THEORY OF TYPE B VIA QUANTUM SYMMETRIC PAIRS Huanchen BAO, Weiqiang WANG Abstracts

摘要

We show that Hecke algebra of type B and a coideal subalgebra 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 bases 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 BGG category O of the ortho-symplectic Lie superalgebras osp(2 m +1 vertical bar 2 n). In particular, our approach provides a new formulation of the Kazhdan- Lusztig theory for Lie algebras of type B/C.