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New approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs / Huanchen Bao and Weiqiang Wang.

By: Bao, Huanchen [author].
Contributor(s): Wang, Weiqiang [author].
Material type: TextTextSeries: Asterisque, 402.Publisher: Paris : Societe Mathematique de France, 2018Description: vii, 134 pages ; 24 cm.ISBN: 9782856298893.Subject(s): Kazhdan-Lusztig polynomials | Lie superalgebras | Hecke algebras | Quantum groupsDDC classification: 510=4 Summary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
510=4 As853 (Browse shelf) Checked out 08/11/2019 C26643
Total holds: 0

Includes bibliographical references.

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.

Abstract also in French.

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