# Research

### Research Interests

Generally speaking, I am interested in Representation Theory and Quantum Algebras.

More specifically, my current research interests are: Bethe ansatz method, Representation Theory of Quantum Groups, Lie Algebras and Superalgebras, and Integrable System.

### Preprints

See also arXiv

*Fine gradings of complex simple Lie algebras and Finite Root Systems*

(with Gang Han, Jun Yu), 29 Oct. 2014. (arXiv:1410.7945) not for publication.

### Publications

See also MathSciNet.

*On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains*

J. High Energ. Phys.**04**, Article number: 120 (2023), (arXiv:2209.14416)*Schur-Weyl duality for quantum toroidal superalgebras*

J. Pure Appl. Algebra**227**(2023), no. 9, 107382, (arXiv:2109.09005)*Completeness of Bethe ansatz for Gaudin models associated with $\mathfrak{gl}(1|1)$*

Nuclear Phys. B**980**(2022), Paper No. 115790, 23 pp (arXiv:2202.08162)*A note on odd reflections of super Yangian and Bethe ansatz*

Lett. Math. Phys.**112**(2022), Article no.: 29 (arXiv:2111.10655)*Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra*

Lett. Math. Phys.**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), Commun. Math. Phys.**386**(2021), 711–747, (arXiv:1910.13360).*Jacobi-Trudi identity and Drinfeld functor for super Yangian*

(with E. Mukhin), Int. Math. Res. Not. IMRN**2021**(2021), no. 21, 16749–16808, (arXiv:2007.15573).*Perfect integrability and Gaudin models*

SIGMA**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), J. Phys. A: Math. Theor.**52**(2019) 375204 (31pp), (arXiv:1811.11225)*On the Gaudin model of type \(G_2\)*

(with E. Mukhin), Commun. Contemp. Math.**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 Colloq.**26**(2019), no. 1, 123-138, (arXiv:1611.03943)*Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus*

SIGMA**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 Appl. Math. Q.**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), J. Math. Phys.**57**(2016), 101703, 23 pages (arXiv:1512.08524)

My Erdös Number: 4.

Paul Erdős–>Shizuo Kakutani–>Karl Endel Petersen–>A. N. Varchenko–>Kang Lu