# 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

*A class of representations for shifted twisted Yangians and affine $\imath$quantum groups*

(with Weiqiang Wang), in preparation*A Drinfeld type presentation of twisted Yangians of quasi-split type*

(with Weinan Zhang), in preparation*Twisted super Yangians of type AIII and their representations*

(arXiv:2311.16373) Updated on 03/04/2024*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