Huanchen Bao, Weiqiang Wang
Published 2013-10-01, updated 2016-01-27Version 2
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.
Comments: v2, 92 pages, References and Notes added, introduction modified, i-canonical bases for based U-modules and positivity of i-KL polynomials added, other minor corrections
Remarks on modules of the ortho-symplectic Lie superalgebras
Crystal basis theory for a quantum symmetric pair $(\mathbf{U},\mathbf{U}^{\jmath})$
Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$
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