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Geometric Schur Duality of Classical Type

- Huanchen Bao, J. Kujawa, Y. Li, W. 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… Expand

50 4- PDF

A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs

- Huanchen Bao, W. 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… Expand

81 4- PDF

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… Expand

26 3- PDF

Canonical bases arising from quantum symmetric pairs

- Huanchen Bao, W. Wang
- Mathematics, Physics
- 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… Expand

46 2- PDF

Multiparameter quantum Schur duality of type B

- Huanchen Bao, W. Wang, H. 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… Expand

14 1- PDF

The m=2 amplituhedron

- Huanchen Bao, X. He
- Mathematics, Physics
- 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… Expand

5- PDF

Canonical bases in tensor products revisited

- Huanchen Bao, H. Wang
- Mathematics
- 1 March 2014

We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig's work.

8- PDF

Canonical bases for tensor products and super Kazhdan-Lusztig theory

- Huanchen Bao, W. Wang, H. Watanabe
- Mathematics
- 1 August 2020

Abstract We generalize a construction in [5] by showing that, for a quantum symmetric pair ( U , U i ) of finite type, the tensor product of a based U i -module and a based U-module is a based U i… Expand

1

Flag manifolds over semifields

- Huanchen Bao, X. He
- Mathematics
- 30 March 2020

In this paper, we develop the theory of flag manifold over a semifield for any Kac-Moody root datum. We show that the flag manifold over a semifield admits a natural action of the monoid over that… Expand

Categorification of quantum symmetric pairs I

- Huanchen Bao, P. Shan, W. Wang, B. Webster
- Mathematics
- 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… Expand

12- PDF

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