A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs
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A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs
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.
Affine Hecke Algebras and Quantum Symmetric Pairs
Author: Zhaobing Fan
language: en
Publisher: American Mathematical Society
Release Date: 2023-01-18
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Affine Flag Varieties and Quantum Symmetric Pairs
Author: Zhaobing Fan
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-09-28
The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.