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. Twisted super Yangians of type AIII and their representations
    (arXiv:2311.16373), submitted
  3. A Drinfeld type presentation of twisted Yangians of quasi-split type
    (with Weinan Zhang), (arXiv:2408.06981), submitted
  4. Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations
    (with Weiqiang Wang and Weinan Zhang), (arXiv:2406.05067), submitted
  5. A Drinfeld type presentation of twisted Yangians
    (with Weiqiang Wang and Weinan Zhang), (arXiv:2308.12254), submitted

Publications

See also MathSciNet.

  1. Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
    Int. Math. Res. Not. IMRN, (arXiv:2308.12484)
  2. On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
    Journal of High Energy Physics 04 (2023), Article number: 120, (arXiv:2209.14416)
  3. Schur-Weyl duality for quantum toroidal superalgebras
    Journal of Pure and Applied Algebra 227 (2023), no. 9, 107382, (arXiv:2109.09005)
  4. 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)
  5. A note on odd reflections of super Yangian and Bethe ansatz
    Letters in Mathematical Physics 112 (2022), Article no.: 29 (arXiv:2111.10655)
  6. Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
    Letters in Mathematical Physics 111 (2021), Article no.: 145 (arXiv:2103.08758).
  7. Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces (with E. Mukhin)
    Annales Henri Poincaré 22 (2021), 4087–4130, (arXiv:2103.16729).
  8. 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).
  9. 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).
  10. Perfect integrability and Gaudin models
    Symmetry, Integrability and Geometry: Methods and Applications 16 (2020), 132, 10 pages, (arXiv:2008.06825).
  11. 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)
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. 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

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