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

  1. On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
    Sept. 28 2022, (arXiv:2209.14416),   New Version
  2. Schur-Weyl duality for quantum toroidal superalgebras
    Sept. 21 2021, (arXiv:2109.09005)
  3. 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 (arXiv:1410.7945) not for publication.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.

  1. 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)
  2. A note on odd reflections of super Yangian and Bethe ansatz
    Lett. Math. Phys. 112 (2022), Article no.: 29 (arXiv:2111.10655)
  3. Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
    Lett. Math. Phys. 111 (2021), Article no.: 145 (arXiv:2103.08758).
  4. Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces
    (with E. Mukhin), Annales Henri Poincaré 22 (2021), 4087–4130 , (arXiv:2103.16729).
  5. 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).
  6. 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).
  7. Perfect integrability and Gaudin models
    SIGMA 16 (2020), 132, 10 pages, (arXiv:2008.06825).
  8. 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)
  9. On the Gaudin model of type \(G_2\)
    (with E. Mukhin), Commun. Contemp. Math. 21 (2019), no. 3, 1850012, 31 pages, (arXiv:1711.02511)
  10. 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)
  11. Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
    SIGMA 14 (2018), 046, 15 pages, (arXiv:1710.06534)
  12. 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)
  13. 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)