Research
Research Interests
Generally speaking, I am interested in Representation Theory, Quantum Algebra, and Mathematical Physics.
More specifically, my current research interests are:
- Drinfeld presentation of twisted Yangians and affine $\imath$quantum groups
- Twisted Yangians and finite $\mathcal W$-algebras of classical type
- Quantum affine/toroida superalgebras and (affine) super Yangians
- Bethe ansatz and quantum integrable systems
- Gaudin models and Heisenberg XXX, XXZ spin chains
Preprints
See also arXiv
- Twisted super Yangian of quasi-split type A, submitted
- Twisted super Yangians of type AIII and their representations
(arXiv:2311.16373), submitted - A Drinfeld type presentation of twisted Yangians of quasi-split type
(with Weinan Zhang), (arXiv:2408.06981), submitted - Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations
(with Weiqiang Wang and Weinan Zhang), (arXiv:2406.05067), submitted - Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
(arXiv:2308.12484), submitted - A Drinfeld type presentation of twisted Yangians
(with Weiqiang Wang and Weinan Zhang), (arXiv:2308.12254), submitted
Publications
See also MathSciNet.
- On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
Journal of High Energy Physics 04 (2023), Article number: 120, (arXiv:2209.14416) - Schur-Weyl duality for quantum toroidal superalgebras
Journal of Pure and Applied Algebra 227 (2023), no. 9, 107382, (arXiv:2109.09005) - Completeness of Bethe ansatz for Gaudin models associated with $\mathfrak{gl}(1|1)$
Nuclear Physics B 980 (2022), Paper No. 115790, 23 pp (arXiv:2202.08162) - A note on odd reflections of super Yangian and Bethe ansatz
Letters in Mathematical Physics 112 (2022), Article no.: 29 (arXiv:2111.10655) - Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
Letters in Mathematical Physics 111 (2021), Article no.: 145 (arXiv:2103.08758). - Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces (with E. Mukhin)
Annales Henri Poincaré 22 (2021), 4087–4130, (arXiv:2103.16729). - On the supersymmetric XXX spin chains associated to $\mathfrak{gl}_{1|1}$ (with E. Mukhin)
Communications in Mathematical Physics 386 (2021), 711–747, (arXiv:1910.13360). - Jacobi-Trudi identity and Drinfeld functor for super Yangian (with E. Mukhin)
International Mathematics Research Notices 2021 (2021), no. 21, 16749–16808, (arXiv:2007.15573). - Perfect integrability and Gaudin models
Symmetry, Integrability and Geometry: Methods and Applications 16 (2020), 132, 10 pages, (arXiv:2008.06825). - Solutions of \(\mathfrak{gl}_{m|n}\) XXX Bethe ansatz equation and rational difference operators (with Chenliang Huang, E. Mukhin)
Journal of Physics A: Mathematical and Theoretical 52 (2019) 375204 (31pp), (arXiv:1811.11225) - On the Gaudin model of type \(G_2\) (with E. Mukhin)
Communications in Contemporary Mathematics 21 (2019), no. 3, 1850012, 31 pages, (arXiv:1711.02511) - Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root systems (with Gang Han, Yucheng Liu)
Algebra Colloquium 26 (2019), no. 1, 123-138, (arXiv:1611.03943) - Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
Symmetry, Integrability and Geometry: Methods and Applications 14 (2018), 046, 15 pages, (arXiv:1710.06534) - Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\) (with E. Mukhin, A. Varchenko)
Pure and Applied Mathematics Quarterly 13 (2017), no.2, 291 – 335 , a special issue of in honor of Yuri Manin’s 80-th birthday, (arXiv:1705.02048) - On the Gaudin model associated to Lie algebras of classical types (with E. Mukhin, A. Varchenko)
Journal of Mathematical Physics 57 (2016), 101703, 23 pages (arXiv:1512.08524)
Collaborators
- Gang Han
- Chenliang Huang
- Yucheng Liu
- Evgeny Mukhin
- Yung-Ning Peng
- Alexander Varchenko
- Weiqiang Wang
- Weinan Zhang
My Erdös Number: 4.
Paul Erdős–>Shizuo Kakutani–>Karl Endel Petersen–>A. N. Varchenko–>Kang Lu