132 citations · 294 across the 20 of their papers we have counts for
21 papers
Double Bruhat cells in symmetric spaces
Huanchen Bao, Jinfeng Song
This paper studies the closures of the double Bruhat cells of symmetric spacess in its equivariant embeddings. We call them large double Bruhat varieties. Our aim is to establish t…
Total positivity and symmetric spaces
Huanchen Bao
We define a notion of total positivity for the symmetric space by taking the Hausdorff closure of the image of Lusztig's totally positive part in . We introduce…
Acyclic matchings on Bruhat intervals and applications to total positivity
Huanchen Bao, Xuhua He
The existence of acyclic complete matchings on the face poset of a regular CW complex implies that the underlying topological space of the CW complex is contractible by discrete Mo…
Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs
Huanchen Bao, Jinfeng Song
Let be a connected reductive algebraic group over an algebraically closed field of characteristic . Let be a quasi-split symmetric subgroup of $…
Total positivity in twisted product of flag varieties
Huanchen Bao, Xuhua He
We show that the totally nonnegative part of the twisted product of flag varieties of a Kac-Moody group admits a cellular decomposition, and the closure of each cell is a topologic…
Product structure and regularity theorem for totally nonnegative flag varieties
Huanchen Bao, Xuhua He
The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) -tota…
A Birkhoff-Bruhat Atlas for partial flag varieties
Huanchen Bao, Xuhua He
A partial flag variety of a Kac-Moody group has a natural stratification into projected Richardson varieties. When is a connected reductive group, a Bruh…
Flag manifolds over semifields
Huanchen Bao, Xuhua He
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…
Quantum symmetric pairs at roots of
Huanchen Bao, Thomas sale
A quantum symmetric pair is a quantization of the symmetric pair of universal enveloping algebras. Recent development suggests that most of the theory for quantum groups can be gen…
The m=2 amplituhedron
Huanchen Bao, Xuhua He
The (tree) amplituhedron is introduced by Arkani-Hamed and Trnka in 2013 in the study of supersymmetric Yang-Mills theory. It is defined in…
Canonical bases arising from quantum symmetric pairs of Kac-Moody type
Huanchen Bao, Weiqiang Wang
For quantum symmetric pairs of Kac-Moody type, we construct canonical bases for the highest weight integrable -modules and the…
Positivity of -canonical bases
Huanchen Bao
For the quantum symmetric pair of type AIII/AIV, we show various positivity properties of the -canonical bases on finite-dimensional sim…
Canonical bases for tensor products and super Kazhdan-Lusztig theory
Huanchen Bao, Weiqiang Wang, Hideya Watanabe
We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based -module and a based -module is a based $\te…
A categorification of Hecke algebras with parameters 1 and v
Huanchen Bao
We categorify the Hecke algebra with parameters 1 and v using a variation of the category of Soergel bimodules.
Canonical bases arising from quantum symmetric pairs
Huanchen Bao, Weiqiang Wang
We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical ba…
Multiparameter quantum Schur duality of type B
Huanchen Bao, Weiqiang Wang, Hideya Watanabe
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 -canonical…
Femtosecond dynamics of correlated many-body states in C fullerenes
Sergey Usenko, Michael Schüler, Armin Azima +7
Fullerene complexes may play a key role in the design of future molecular electronics and nanostructured devices with potential applications in light harvesting using organic solar…
Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs
Huanchen Bao
We reformulate the Kazhdan-Lusztig theory for the BGG category of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initia…
Geometric Schur duality of classical type
Huanchen Bao, Jonathan Kujawa, Yiqiang Li +1
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 stabili…
Canonical bases in tensor products revisited
Huanchen Bao, Weiqiang Wang
We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig's work.
A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
Huanchen Bao, Weiqiang Wang
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…