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.

Publications

  1. On the Gaudin model of type \(G_2\)
    (with E. Mukhin), Commun. Contemp. Math. (arXiv:1711.02511)
  2. Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
    SIGMA 14 (2018), 046, 15 pages, (arXiv:1710.06534)
  3. 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 no.2 (2017), a special issue of in honor of Yuri Manin’s 80-th birthday, (arXiv:1705.02048)
  4. On the Gaudin model associated to Lie algebras of classical types
    (with E. Mukhin, A. Varchenko), J. Math. Phys. 57, 101703 (2016) (arXiv:1512.08524)

Preprints

  1. Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root systems
    (with Gang Han, Yucheng Liu), 12 Nov. 2016, (arXiv:1611.03943), submitted
  2. Fine gradings of complex simple Lie algebras and Finite Root Systems
    (with Gang Han, Jun Yu), 29 Oct. 2014. (arXiv:1410.7945)

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