New approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs - Bao, Huanchen; Wang, Weiqiang (Paris : Societe Mathematique de France, 2018)
We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify 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 orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.
Includes bibliographical references.
Abstract also in French.
Keywords: Kazhdan-Lusztig polynomials; Lie superalgebras; Hecke algebras; Quantum groups