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

Huanchen Bao University of Maryland, College Park Weiqiang Wang university of Virginia

Representation Theory mathscidoc:1804.30001

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 $\mathfrak{osp}(2m+1|2n)$. In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.
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  • To appear in Asterisque
@inproceedings{huanchena,
  title={A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs},
  author={Huanchen Bao, and Weiqiang Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180410023419460959034},
}
Huanchen Bao, and Weiqiang Wang. A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180410023419460959034.
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