HECHUN ZHANG

Professor Department of mathematical sciences, Tsinghua University, Beijing100084, P.R.China Tel: Fax: +86(0)1062781785 Email:mailto:hzhang@math.tsinghua.edu.cn

My CV

• Education
  • Jul.1987-Jul.1990, Ph.D. student in Institute of Systems Science at Institute of Systems Science.

       Supervisor: Professor Zhexian Wan.

  • Jul.1984-Jul.1987, Graduate student in Department of Mathematics at Hebei Normal University.

       Supervisor: Professor Wang Yangxian.

  • Sept.1980-Jul.1984, UnderGraduate student at Department of Mathematics at Hebei Normal University.

• Perfessional background
  • Dec.2002- \present, Professor in Department of Mathematical Sciences at Tsinghua University.
  • Jan., 2002-Dec.2002, Visiting professor in University of Amsterdam.
  • Sep.1999-Sep.2000, Foreign Professor in Institute of Mathematics at University of Tsukuba.
  • May1995-May1997, Postdoc in Depart,ment of Mathematics at University of Copenhagen.

My Research Interests

• Representation Theory of quantum groups: Root of unity and DKP conjecture; Canonical basis and dual canonical basis.

• Infinite dimensional Lie algebras: Kac moody algebras; Virasoro algebra.

My Papers and Preprints

1. Hechun Zhang, Some Properties of $g(A)$ Modules. (Chinese) Chinese Sci.Bull 32, no 17, 1288-1290, 1987.
   
2. Hechun Zhang, Imaginary Root Systems of Kac-Moody Algebras. (Chinese)Acta Math. Sinica 33,no 1,1-6. 1990.
   
3. Hechun Zhang, Universal Integrable Representations of Kac-Moody Algebras. Chinese Sci.Bull 36, No 6, 445-448, 1991.
   
4. Hechun Zhang, The Reducibility of Universal Integrable Representations. Chinese Sci.Bull vol. 36(24), 1844-1846, 1991.
   
5. Hechun Zhang, Kaiming Zhao, Root Systems of A Class of Kac-Moody Algebras. Algebra Colloq. 1, no.4,359-368, 1994.
   
6. Hechun Zhang, Some Remarks on Imaginary Roots. Chinese Sci.Bull.40, no.10 793-796, 1995.
   
7. Hechun Zhang, Weights of Integerable Modules.(Chinese) Acta Math. Sinica 38,no 1, 30-37, 1995.
   
8. Hechun Zhang, Kaiming Zhao, A Class of Representation of the Virasoro-like Algebras. Comm. in Alg. vol. 24(14),4361-4372, 1996.
   
9. 9. Caihui Lu, Hechun Zhang, Kaiming Zhao, Lie Algebras in China, In " Group Theory in China" Z. Wan and S. Shi Eds. Kluwer Academic Publishers, 1996.
   
10. Hechun Zhang, A class of representations of the Virasoro algebra. J. Alg. vol. 190,1-10, 1997.
    
11. H.P. Jakobsen, Hechun Zhang, The center of the quantized matrix alegbra. J. Alg,196,458-474, 1997.
    
12. H. P. Jakobsen, Hechun Zhang, The center of the quantized Dipper-Donkin matrix algebra. Beit. zur Alg. und Geom. 38, No. 2, 411-421, 1997.
    
13. Hechun Zhang, Witt-Like Algebras and Their q-Analogues. Linear and Multilinear Algebras, 42,221-231, 1997.
    
14. H.P. Jakobsen, A. Jensen, S. J\o ndrup, Hechun Zhang, Quadratic Algebras of Type A III (I). Tsinghua Science and Technology, Vol. 4, 1076-1084, 1998.
    
15. H.P. Jakobsen, A. Jensen, S. J\o ndrup, Hechun Zhang, Quadratic Algebras of Type A III (II). Tsinghua Science and Technology, Vol. 4, 1085-1092, 1998.
    
16. H.P. Jakobsen, S. J\o ndrup, Hechun Zhang, Quadratic Algebras of Type A III (III). Tsinghua Science and Technology, Vol. 4, 1093-1099, 1998.
    
17. H.P. Jakobsen, Hechun Zhang, The cyclic representation of the quantum matrix algebra. Comm. in Alg. Vol. 27, No. 2, 493-510, 1999.
    
18. Hechun Zhang, The representations of the coordinate ring of the quantum symplectic space. Journal of Pure and applied algebra, Vol. 150, no. 1, 95-106, 2000.
    
19. H.P. Jakobsen, Hechun Zhang, A class of quadratic matrix algebras arising from the quantized enveloping algebra ${\s U}_q(A_{2n-1})$, J. of Math. Phys., Vol. 41, Issue 4, 2310-2336, 2000.
    
20. H.P. Jakobsen, Hechun Zhang, Quantized Heisenberg Space, Algebras and Representation Theory, Vol. 3, Issue 2, 151-174, 2000.
    
21. Yucai Su, Xiaoping Xu, Hechun Zhang, Derivation-Simple algebras and the structures of Generaliized Lie algebras of Witt type. J. Alg. Vol. 233, No. 2, 642-662, 2000.
    
22. Hechun Zhang, The representations of the coordinate ring of the quantum matrix, Algebra Colloquium,Vol. 9, No. 4, 283-292,2002.
    
23. Hechun Zhang, The inverse of a real generalized Cartan matrix. To appear in Linear and Multilinear algebra.
    

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