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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

  1. Perfect integrability and Gaudin models
    Aug. 17, 2020, (arXiv:2008.06825).
  2. Jacobi-Trudi identity and Drinfeld functor for super Yangian
    (with E. Mukhin), Jul. 31, 2020. (arXiv:2007.15573).   Updated Version (07/31/2020)
  3. On the supersymmetric XXX spin chains associated to $\mathfrak{gl}_{1|1}$
    (with E. Mukhin), Oct. 29, 2019. (arXiv:1910.13360), submitted.
  4. 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 (arXiv:1410.7945) not for publication.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

  1. 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)
  2. On the Gaudin model of type \(G_2\)
    (with E. Mukhin), Commun. Contemp. Math. 21 (2019), no. 3, 1850012, 31 pages, (arXiv:1711.02511)
  3. 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)
  4. Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
    SIGMA 14 (2018), 046, 15 pages, (arXiv:1710.06534)
  5. 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)
  6. 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)