A new approach to Kazhdan-Lusztig theory of type ${\bf B}$ via quantum symmetric pairs

By Huanchen Bao, Weiqiang Wang. Astérisque, 2013

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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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c5b869e892cc0b66aa90abb2d0bf3578603aae28

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Citations in the corpus

Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, background): “It generalizes Lusztig’s bar involution and should be compared with the bar involution in [11].”
Affine flag varieties and quantum symmetric pairs (2016, unknown): “S AND QUANTUM SYMMETRIC PAIRS 5 ask for generalization of the above type Aconstructions to other, say classical, types. The progress in this direction has been made only in recent years. Motivated by [BW13], Bao, Kujawa, and two of the authors [BKLW14, BLW14] provided a geometric construction of Sch”