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Geometric Schur Duality of Classical Type
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 inExpand
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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 satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group ofExpand
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Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs
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 WeiqiangExpand
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Canonical bases arising from quantum symmetric pairs
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 basesExpand
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Multiparameter quantum Schur duality of type B
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 tensorExpand
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The m=2 amplituhedron
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 theExpand
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Canonical bases in tensor products revisited
We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig's work.
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Canonical bases for tensor products and super Kazhdan-Lusztig theory
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 iExpand
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Flag manifolds over semifields
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 thatExpand
Categorification of quantum symmetric pairs I
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 $1$-morphismsExpand
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