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

1. Twisted super Yangian of quasi-split type A, submitted
2. A Drinfeld type presentation of twisted Yangians of quasi-split type
   (with Weinan Zhang), (arXiv:2408.06981), submitted
3. A Drinfeld type presentation of twisted Yangians
   (with Weiqiang Wang and Weinan Zhang), (arXiv:2308.12254), submitted
4. Shifted twisted Yangians and fixed point loci of affine Grassmannian slices
   (with Weiqiang Wang and Alex Weekes), in preparation
5. Shifted twisted Yangians and finite W-algebras of classical type
   (with Yung-Ning Peng, Lukas Tappeiner, Lewis Topley and Weiqiang Wang), draft finished, 88 pages.

Publications

See also MathSciNet.

1. Twisted super Yangians of type AIII and their representations
   to appear in Journal of Algebra, (arXiv:2311.16373)
2. Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations (with Weiqiang Wang and Weinan Zhang)
   Communications in Mathematical Physics, 406 (2025), no. 5, article no. 98, (arXiv:2406.05067)
3. Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
   International Mathematics Research Notices, 2024 (2024), no. 24, pp. 14519-14542 (arXiv:2308.12484)
4. On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
   Journal of High Energy Physics 04 (2023), Article number: 120, (arXiv:2209.14416)
5. Schur-Weyl duality for quantum toroidal superalgebras
   Journal of Pure and Applied Algebra 227 (2023), no. 9, 107382, (arXiv:2109.09005)
6. 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)
7. A note on odd reflections of super Yangian and Bethe ansatz
   Letters in Mathematical Physics 112 (2022), Article no.: 29 (arXiv:2111.10655)
8. Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
   Letters in Mathematical Physics 111 (2021), Article no.: 145 (arXiv:2103.08758).
9. Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces (with E. Mukhin)
   Annales Henri Poincaré 22 (2021), 4087–4130, (arXiv:2103.16729).
10. 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).
11. 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).
12. Perfect integrability and Gaudin models
    Symmetry, Integrability and Geometry: Methods and Applications 16 (2020), 132, 10 pages, (arXiv:2008.06825).
13. 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)
14. 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)
15. 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)
16. 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)
17. 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)
18. 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

Zhejiang University

Chenliang Huang

Deloitte

Yucheng Liu

~

Evgeny Mukhin

Indiana University Indianapolis

Yung-Ning Peng

National Cheng Kung University

Lukas Tappeiner

University of Bath

Lewis Topley

University of Bath

Alexander Varchenko

University of North Carolina at Chapel Hill

Weiqiang Wang

University of Virginia

Alex Weekes

University of Saskatchewan

Weinan Zhang

University of Hong Kong

My Erdös Number: 4.
Paul Erdős–>Shizuo Kakutani–>Karl Endel Petersen–>A. N. Varchenko–>Kang Lu