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Hechun Zhang

Ph.D. Professor
Institute of Pure Mathematics
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China
Fax: +86(10)62781785
Email: hzhang@math.tsinghua.edu.cn

EDUCATION                                                                                     Wan’s Conference (中文版   English Version )

July.1987-July.1990, Ph.D. student in Institute of Systems Science at Institute of Systems Science.
Supervisor: Professor Zhexian Wan.

July.1984-July.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.

PROFESSIONAL BACKGROUND

Jan., 2002-Dec., 2002, Visiting professor in University of Amsterdam,
Dec., 2002- , Professor in
Department of Mathematical Sciences at Tsinghua University.
Sep., 1999-Sep., 2000, Foreign Professor in Institute of Mathematics at University of Tsukuba.
May, 1995-May,1997, Postdoc in Depart,ment of Mathematics at University of Copenhagen.

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.

TEACHINGS

Fall 2003
Linear Algebras(I).

 

MAIN PUBLICATIONS

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. 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.

24. Zhang, Hechun, On dual canonical bases. J. Phys. A  37  (2004),  no. 32, 7879--7893.

25. Zhang, Hechun, Zhang, R. B.,  Dual canonical bases for the quantum special linear group and invariant subalgebras. Lett. Math. Phys.  {\bf 73} (2005),165 -181.

26. Zhang Hechun and Zhang, R. B.Dual canonical bases for the quantum general linear supergroup. To appear in J. Algebra.

27. H. P. Jakobsen and hechun Zhang, The exponential nature and positivity. To appear in Algebras and Representation Theory.

PREPRINTS

Zhang, Hechun and  Zhang, R. B., Kazhdan-Lusztig polynomials and canonical basis for general linear quantum super-groups.

LINKS

Algebra and Representation in Tsinghua University
Department of Mathematical Sciences
Tsinghua University
Fdlist at Fakultaet fuer Mathematik, Universitaet Bielefeld


updated in Nov. 2003.