Corpus ID: 118498353

A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs

@inproceedings{Bao2018ANA,
  title={A New Approach to Kazhdan-lusztig Theory of Type \$b\$ Via Quantum Symmetric Pairs},
  author={Huanchen Bao and Weiqiang Wang},
  year={2018}
}
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… Expand