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

Author: Huanchen Bao; Weiqiang Wang
Publisher: Paris : Société Mathématique de France, 2018. ©2018
Series: Astérisque, 402.
Edition/Format:   Print book : EnglishView all editions and formats
Publication:Astérisque, no:402
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  Read more...
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Document Type: Book
All Authors / Contributors: Huanchen Bao; Weiqiang Wang
ISBN: 9782856298893 2856298893
OCLC Number: 1059488257
Language Note: Abstract also in French.
Description: vii, 134 pages ; 24 cm.
Series Title: Astérisque, 402.
Responsibility: Huanchen Bao, Weiqiang Wang.

Abstract:

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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