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A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs
- Huanchen Bao, Weiqiang Wang
- Mathematics
- 1 October 2013
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…
Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs
- Huanchen Bao
- Mathematics
- 16 March 2016
We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang…
Geometric Schur Duality of Classical Type
- Huanchen Bao, J. Kujawa, Yiqiang Li, Weiqiang Wang
- Mathematics
- 15 April 2014
This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in…
Canonical bases arising from quantum symmetric pairs
- Huanchen Bao, Weiqiang Wang
- Mathematics
- 28 October 2016
We develop a general theory of canonical bases for quantum symmetric pairs $$({\mathbf{U}}, {\mathbf{U}}^\imath )$$(U,Uı) with parameters of arbitrary finite type. We construct new canonical bases…
Canonical bases for tensor products and super Kazhdan-Lusztig theory
- Huanchen Bao, Weiqiang Wang, Hideya Watanabe
- MathematicsJournal of Pure and Applied Algebra
- 28 August 2018
We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based…
Categorification of quantum symmetric pairs I
- Huanchen Bao, P. Shan, Weiqiang Wang, B. Webster
- MathematicsQuantum Topology
- 12 May 2016
We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms…
A Birkhoff–Bruhat atlas for partial flag varieties
- Huanchen Bao, Xuhua He
- Mathematics
- 20 July 2020
Multiparameter quantum Schur duality of type B
- Huanchen Bao, Weiqiang Wang, Hideya Watanabe
- Mathematics
- 6 September 2016
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the $\imath$-canonical basis on the tensor…
Canonical bases arising from quantum symmetric pairs of Kac–Moody type
- Huanchen Bao, Weiqiang Wang
- MathematicsCompositio Mathematica
- 24 November 2018
For quantum symmetric pairs $(\textbf {U}, \textbf {U}^\imath )$ of Kac–Moody type, we construct $\imath$-canonical bases for the highest weight integrable $\textbf U$-modules and their tensor…
The m=2 amplituhedron
- Huanchen Bao, Xuhua He
- Mathematics
- 13 September 2019
The (tree) amplituhedron $\mathcal{A}_{n, k, m}$ is introduced by Arkani-Hamed and Trnka in 2013 in the study of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is defined in terms of the…
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