Research Interests

• Kac-Moody Lie algebras, extended affine Lie algebras, toroidal Lie algebras

• Representation theory, quantum groups, Yangians, vertex operator algebras

• Some other infinite-dimensional Lie algebras: Witt algebra, Virasoro algebra and so on

• Lie algebras and superalgebras associated with left-symmetric algebraic structures

Publications/Preprints

1. H. Chen, Y. Gao and A. Pianzola, Irreducible representations of Lie algebras \(\mathfrak{gl}_{m+n}(\mathbb{C})\) and \(\widehat{\mathfrak{gl}_{m+n}(\mathbb{C})}\), in preparation.
   
   
2. H. Chen, Y. Gao and S. Shi, Imaginary Whittaker modules for a class of extended affine Lie algebras, in preparation.
   
   
3. H. Chen and H. He, The \(q\)-Virasoro-like algebra and some simple quotients, in preparation.
   
   
4. H. Chen and Z. Zeng, Irreducible representations of Lie algebras \(\mathfrak{gl}_{m|n}(\mathbb{C})\) and \(\widehat{\mathfrak{gl}_{m|n}(\mathbb{C})}\), in preparation.
   
   
5. H. Chen and Q. Wang, Irreducible representations of supersolvable Lie superalgebras, in preparation.
   
   
6. H. Chen, W. Liu and Q. Wang, A class of new modular Lie superalgebras and their representations, in preparation.
   
   
7. H. Chen and Q. Wang, Invariant rings of Lie superalgebras of Cartan type over fields of characteristic zero, in preparation.
   
   
8. H. Chen, Y. Gao and Z. Zeng, Some representations of quantum enveloping superalgebra \(U_q(\mathfrak{gl}_{M|N}(\mathbb{C}))\), in preparation.
   
   
9. H. Chen, Q. Wang and J. Zhang, Left-symmetric algebra structures on the Lie algebra \(V(0,\frac{p}{q})\), in preparation.
   
   
10. H. Chen, L. Ge, Z. Li, and L. Wang, Classical Whittaker modules for the affine Kac-Moody algebra \(A_{N}^{(1)}\), in preparation.
    
    
11. H. Chen and Z. Wan, A class of representations over the Euclidean Lie algebra \(\mathfrak{e}_3\) and the irreducible representations of \(\mathfrak{sl}_2(\mathbb{C})\), submitted.
    
    
12. S. Bhargava, H. Chen and Y. Gao, Finite dimensional representations of the nullity 2 centreless core \(\mathfrak{g}_{2n;\rho}(\mathbb{C}_q)\), submitted.
    
    
13. H. Chen and X. Liu, Semi-direct product Lie algebras \(\mathfrak{sl}_2(\mathbb{C}) \ltimes V(m)\) and representations, submitted.
    
    
14. H. Chen, X. Liu and L. Wang, \(U^0\)-free quantum group representations, submitted.
    
    
15. H. Chen, and Z. Li, A unitary representation of the extended affine Lie algebra, to appear in Algebra Colloquium.
    
    
16. H. Chen, and O. Hassan, Left-symmetric superalgebra structures on an infinite-dimensional Lie superlagebra7, to appear in Algebra Colloquium.
    
    
17. H. Chen, H. Dan and X. Liu, A class of polynomial modules over map Lie algebras, to appear in Communications in Mathematics and Statistics.
    
    
18. H. Chen and Q. Chen, Finite dimensional representations of the \(\mathrm{BC}\)-graded Lie algebra \(\mathfrak{g}_{2n+1}(\mathbb{C}_q)\), to appear in Frontiers of Mathematics.
    
    
19. H. Chen and L. Wang, Whittaker modules over some generalized Weyl algebras,to appear in Algebras and Representation Theory.
    
    
20. H. Chen and L. Wang, A family of simple modules over the Rueda's algebras, Journal of Algebra 591 (2022) 360-378.
    
    
21. Y. Cai, H. Chen, X. Guo, Y. Ma and M. Zhu, A class of non-weight modules of \(U_q(\mathfrak{sl}_2)\) and Clebsch-Gordan type formulas, Forum Mathematicum 33(2021) 743-755.
    
    
22. Y. Wang, H. Chen and Y. Gao, A family of representations of the affine Lie superalgebra \(\widehat{\mathfrak{gl}_{m|n}(\mathbb{C})}\), Journal of Algebra 492 (2017) 371-392.
    
    
23. H. Chen, X. Guo, Non-weight modules over the Heisenberg–Virasoro algebra and the \(W\) algebra \(W(2,2)\), Journal of Algebra and Its Applications 16 (2017) 1750097 16pp.
    
    
24. H. Chen, X. Guo, A new family of modules over the Virasoro algebra, Journal of Algebra 457 (2016) 73-105.
    
    
25. Q. Wang, H. Chen and W. Liu, On representations of the filiform Lie superalgebra \(L_{m,n}\), Journal of Geometry and Physics 97 (2015) 93-104.
    
    
26. H. Chen and J. Sun, Universal central extensions of \(\mathfrak{sl}_{m|n}\) over \(\mathbb{Z}/2\mathbb{Z}\)-graded algebras, Journal of Pure and Applied Algebra 219 (2015) 4278–4294.
    
    
27. H. Chen, X. Guo and K. Zhao, Irreducible quasifinite modules over a class of Lie algebras of block type, The Asian Journal of Mathematics 18 (2014) 817–828.
    
    
28. H. Chen, N. Guay and X. Ma, Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type \(BC\), Transactions of the American Mathematical Society 366 (2014) 2517–2574.
    
    
29. H. Chen and J. Li, Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra, Science in China Series A: Mathematics 57 (2014) 469–476.
    
    
30. H. Chen, X. Guo and K. Zhao, Tensor product weight modules over the Virasoro algebra, Journal of the London Mathematical Society 88 (2013) 829-844.
    
    
31. H. Chen and X. Guo, New simple modules for the Heisenberg-Virasoro algebra, Journal of Algebra 390 (2013) 77-86.
    
    
32. S. Bhargava, H. Chen and Y. Gao, A family of representations of the Lie superalgebra \(\widehat{\mathfrak{gl}_{1|l-1}(\mathbb{C}_q)}\), Journal of Algebra 386 (2013) 61-76.
    
    
33. H. Chen and X. Guo, Unitary Harish-Chandra modules over Block type Lie algebras \(B(q)\), Journal of Lie Theory 23 (2013) 827-836.
    
    
34. H. Chen and N. Guay, Central extensions of matrix Lie superalgebras over \(\mathbb{Z}/2 \mathbb{Z}\)-graded algebras, Algebras and Representation Theory 16 (2013) 591-604.
    
    
35. H. Chen and J. Li, Left-symmetric algebraic structures on the \(W\)-algebra \(W(2;2)\), Linear Algebras and its Applications 437 (2012) 1821-1834.
    
    
36. H. Chen and N. Guay, Twisted affine Lie superalgebra of type \(Q\) and quantization of its enveloping superalgebra, Mathematische Zeitschrift 272 (2012) 317-347.
    
    
37. X. Kong, H. Chen and C. Bai, Classification of graded left-symmetric algebraic structures on Witt and Virasoro algebras, International Journal of Mathematics 22 (2011) 201-222.
    
    
38. S. Shang, H. Chen and Y. Gao, Central extensions of Steinberg Lie superalgebras of small rank, Communications in Algebra 35 (2007) 4225-4244.
    
    
39. H. Chen and Y. Gao, \(BC_{_N}\)-graded Lie algebras arising from fermionic representations, Journal of Algebra 308 (2007) 545-566.
    
    
40. H. Chen, Y. Gao and S. Shang, \(B(0,N)\)-graded Lie superalgebras coordinatized by quantum tori, Science in China Series A: Mathematics 49 (2006) 1740-1752.



1. H. Chen, Some Root Graded Lie Algebras and their Representations (in Chinese with English abstract), Ph.D. Thesis, University of Science and Technology of China, 2008.

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