Yongchang ZHU
朱永昌
PhD in Mathematics
Yale University, 1990

Professor
Department of Mathematics



(852) 2358 7447
mazhu@ust.hk
Room 3459
Personal Web

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Google Scholar
i0Yurh8AAAAJ

ORCID
0000-0003-2179-3284

Scopus ID
56172333600




Research Interest Publications Projects Teaching Assignment RPG Supervision Space used




Research Interest

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Representation theory
Infinite dimensional lie algebras and groups
Vertex operator algebras
Conformal field theory



Publications

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All Years 27 2022 0 2021 1 2020 0 2019 2 2018 1 2017 0 2016 23

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2021 1

A Construction of Representations of Loop Group and Affine Lie Algebra of sl(n)
Algebras and Representation Theory, 16 March 2021
Dai, Xuanzhong; Zhu, Yongchang Article

2019 2

Addition formula and gamma-factors for local fields
Journal of Number Theory, v. 198, May 2019, p. 52-73
Zhu, Yongchang Article
Selberg Integral Over Local Fields
Forum Mathematicum, 2019
Fu, Zenan; Zhu, Yongchang Article

2018 1

LCA(2), Weil index, and Product Formula
Advances in Mathematics, v. 329, April 2018, p. 1088-1136
Liu, Dongwen; Zhu, Yongchang Article

2014 1

Weil Representations and Theta Functionals on Surfaces
Contemporary Mathematics, v. 610, 2014, p. 353-370
Zhu, Yongchang Conference paper

2013 1

On the Central Charge of a Factorizable Hopf Algebra
Advances in Mathematics, v. 236, March 2013, p. 158-223
Sommerhaeuser, Yorck; Zhu, Yongchang Article

2012 1

Introduction
Memoirs of the American Mathematical Society, v. 219, (1028), 2012, p. 1-140
Sommerhaeuser, Yorck; Zhu, Yongchang Article

2011 2

ON THE SIEGEL-WEIL THEOREM FOR LOOP GROUPS, I
Duke mathematical journal, v. 157, (2), April 2011, p. 283-336
Garland, Howard; Zhu, Yongchang Article
On the Siegel-Weil theorem for loop groups, II
American journal of mathematics, v. 133, (6), 2011, p. 1663-1712
Garland, H.; Zhu, Y. Article

2010 1

On the theta functional of Weil representations for symplectic loop groups
Journal of Algebra, v. 324, (11), 2010, p. 3115-3130
Liu, D.; Zhu, Y. Article

2008 1

Theta functions and Weil representations of loop symplectic groups
Duke mathematical journal, v. 143, (1), 2008, MAY 15, p. 17-39
Zhu, Yongchang Article

2007 1

An Analogue of Satake Transform for p-adic Loop Groups
Proceedings of international congress of Chinese mathematicians,, Vol 2, Dec 17-22, 2007.
Zhu, Yongchang Conference paper

2006 1

On higher Frobenius-Schur indicators
Memoirs of the American Mathematical Society, No. 855, May 2006
Kashina, Y.; Sommerhauser, Y.; Zhu, Yongchang Article

2002 1

Self-dual modules of semisimple Hopf algebras
Journal of algebra, v. 257, (1), 2002, NOV 1, p. 88-96
Kashina, Y.; Sommerhauser, Y.; Zhu, YC Article

2001 3

Hecke algebras and Representation Rings of Hopf algebras
AMS/IP, Studies in Advanced Mathematics, v. 20, 2001
Zhu, Yongchang Article
On Hopf algebras with positive bases
Journal of algebra, v. 237, (2), 2001, MAR 15, p. 421-445
Lu, JH; Yan, M.; Zhu, YC Article
The dimension of irreducible modules for transitive module algebras
Communications in algebra, v. 29, (7), 2001, p. 2877-2886
Zhu, YC Article

2000 2

On the set-theoretical Yang-Baxter equation
Duke mathematical journal, v. 104, (1), 2000, JUL 15, p. 1-18
Lu, JH; Yan, M.; Zhu, YC Article
Quasi-triangular structures on Hopf algebras with positive bases
Contemporary Math., Amer. math. Soc., 2000, p. 339-356
Lu, J.; Yan, M.; Zhu, Yongchang Article

1998 1

Stabilizer for Hopf algebra actions
Communications in algebra, v. 26, (12), 1998, p. 3885-3898
Yan, M.; Zhu, YC Article

1997 1

A commuting pair in Hopf algebras
Proceedings of the American Mathematical Society, v. 125, (10), 1997, OCT, p. 2847-2851
Zhu, Y. Article

1996 1

Modular invariance of characters of vertex operator algebras
Journal of the American Mathematical Society, v. 9, (1), 1996, JAN, p. 237-302
Zhu, YC Article

1994 4

Discrete series of the Virasoro algebra and the moonshine module, In: Algebraic groups and their generalizations: quantum and infinite-dimensional methods
Sympos. Pure Math, v. 56, (2), p. 295-316, AMS 1994
Dong, C.; Mason, G.; Zhu, Yongchang Article
Global Vertex Operators on Riemann Surfaces
Communications in Math. Phys, v. 165, (3), 1994, p. 485-531
Zhu, Yongchang Article
Hopf algebras of prime dimension
Internat. Math. Res. Notices, (1), 1994, p. 53-59
Zhu, Yongchang Article
Weight spaces and root spaces of Kac-Moody algebras
J. Algebra, v. 168, (3), 1994, p. 936-948
Zhu, Yongchang Article

1992 1

Vertex operator algebras associated to representations of affine and Virasoro Algebras
Duke Mathematical Journal, v. 66, p. 123-168, 1992
Frenkel, I.; Zhu, Yongchang Article


Expand All Collapse All


Article 1

A Construction of Representations of Loop Group and Affine Lie Algebra of sl(n)
Algebras and Representation Theory, 16 March 2021
Dai, Xuanzhong; Zhu, Yongchang


Expand All Collapse All


Article 2

Addition formula and gamma-factors for local fields
Journal of Number Theory, v. 198, May 2019, p. 52-73
Zhu, Yongchang
Selberg Integral Over Local Fields
Forum Mathematicum, 2019
Fu, Zenan; Zhu, Yongchang


Expand All Collapse All


Article 1

LCA(2), Weil index, and Product Formula
Advances in Mathematics, v. 329, April 2018, p. 1088-1136
Liu, Dongwen; Zhu, Yongchang


Expand All Collapse All


Conference paper 1

Weil Representations and Theta Functionals on Surfaces
Contemporary Mathematics, v. 610, 2014, p. 353-370
Zhu, Yongchang


Expand All Collapse All


Article 1

On the Central Charge of a Factorizable Hopf Algebra
Advances in Mathematics, v. 236, March 2013, p. 158-223
Sommerhaeuser, Yorck; Zhu, Yongchang


Expand All Collapse All


Article 1

Introduction
Memoirs of the American Mathematical Society, v. 219, (1028), 2012, p. 1-140
Sommerhaeuser, Yorck; Zhu, Yongchang


Expand All Collapse All


Article 2

ON THE SIEGEL-WEIL THEOREM FOR LOOP GROUPS, I
Duke mathematical journal, v. 157, (2), April 2011, p. 283-336
Garland, Howard; Zhu, Yongchang
On the Siegel-Weil theorem for loop groups, II
American journal of mathematics, v. 133, (6), 2011, p. 1663-1712
Garland, H.; Zhu, Y.


Expand All Collapse All


Article 1

On the theta functional of Weil representations for symplectic loop groups
Journal of Algebra, v. 324, (11), 2010, p. 3115-3130
Liu, D.; Zhu, Y.


Expand All Collapse All


Article 1

Theta functions and Weil representations of loop symplectic groups
Duke mathematical journal, v. 143, (1), 2008, MAY 15, p. 17-39
Zhu, Yongchang


Expand All Collapse All


Conference paper 1

An Analogue of Satake Transform for p-adic Loop Groups
Proceedings of international congress of Chinese mathematicians,, Vol 2, Dec 17-22, 2007.
Zhu, Yongchang


Expand All Collapse All


Article 1

On higher Frobenius-Schur indicators
Memoirs of the American Mathematical Society, No. 855, May 2006
Kashina, Y.; Sommerhauser, Y.; Zhu, Yongchang


Expand All Collapse All


Article 1

Self-dual modules of semisimple Hopf algebras
Journal of algebra, v. 257, (1), 2002, NOV 1, p. 88-96
Kashina, Y.; Sommerhauser, Y.; Zhu, YC


Expand All Collapse All


Article 3

Hecke algebras and Representation Rings of Hopf algebras
AMS/IP, Studies in Advanced Mathematics, v. 20, 2001
Zhu, Yongchang
On Hopf algebras with positive bases
Journal of algebra, v. 237, (2), 2001, MAR 15, p. 421-445
Lu, JH; Yan, M.; Zhu, YC
The dimension of irreducible modules for transitive module algebras
Communications in algebra, v. 29, (7), 2001, p. 2877-2886
Zhu, YC


Expand All Collapse All


Article 2

On the set-theoretical Yang-Baxter equation
Duke mathematical journal, v. 104, (1), 2000, JUL 15, p. 1-18
Lu, JH; Yan, M.; Zhu, YC
Quasi-triangular structures on Hopf algebras with positive bases
Contemporary Math., Amer. math. Soc., 2000, p. 339-356
Lu, J.; Yan, M.; Zhu, Yongchang


Expand All Collapse All


Article 1

Stabilizer for Hopf algebra actions
Communications in algebra, v. 26, (12), 1998, p. 3885-3898
Yan, M.; Zhu, YC


Expand All Collapse All


Article 1

A commuting pair in Hopf algebras
Proceedings of the American Mathematical Society, v. 125, (10), 1997, OCT, p. 2847-2851
Zhu, Y.


Expand All Collapse All


Article 1

Modular invariance of characters of vertex operator algebras
Journal of the American Mathematical Society, v. 9, (1), 1996, JAN, p. 237-302
Zhu, YC


Expand All Collapse All


Article 4

Discrete series of the Virasoro algebra and the moonshine module, In: Algebraic groups and their generalizations: quantum and infinite-dimensional methods
Sympos. Pure Math, v. 56, (2), p. 295-316, AMS 1994
Dong, C.; Mason, G.; Zhu, Yongchang
Global Vertex Operators on Riemann Surfaces
Communications in Math. Phys, v. 165, (3), 1994, p. 485-531
Zhu, Yongchang
Hopf algebras of prime dimension
Internat. Math. Res. Notices, (1), 1994, p. 53-59
Zhu, Yongchang
Weight spaces and root spaces of Kac-Moody algebras
J. Algebra, v. 168, (3), 1994, p. 936-948
Zhu, Yongchang


Expand All Collapse All


Article 1

Vertex operator algebras associated to representations of affine and Virasoro Algebras
Duke Mathematical Journal, v. 66, p. 123-168, 1992
Frenkel, I.; Zhu, Yongchang


Expand All Collapse All


2014 1

Weil Representations and Theta Functionals on Surfaces
Contemporary Mathematics, v. 610, 2014, p. 353-370
Zhu, Yongchang Conference paper

2013 1

On the Central Charge of a Factorizable Hopf Algebra
Advances in Mathematics, v. 236, March 2013, p. 158-223
Sommerhaeuser, Yorck; Zhu, Yongchang Article

2012 1

Introduction
Memoirs of the American Mathematical Society, v. 219, (1028), 2012, p. 1-140
Sommerhaeuser, Yorck; Zhu, Yongchang Article

2011 2

ON THE SIEGEL-WEIL THEOREM FOR LOOP GROUPS, I
Duke mathematical journal, v. 157, (2), April 2011, p. 283-336
Garland, Howard; Zhu, Yongchang Article
On the Siegel-Weil theorem for loop groups, II
American journal of mathematics, v. 133, (6), 2011, p. 1663-1712
Garland, H.; Zhu, Y. Article

2010 1

On the theta functional of Weil representations for symplectic loop groups
Journal of Algebra, v. 324, (11), 2010, p. 3115-3130
Liu, D.; Zhu, Y. Article

2008 1

Theta functions and Weil representations of loop symplectic groups
Duke mathematical journal, v. 143, (1), 2008, MAY 15, p. 17-39
Zhu, Yongchang Article

2007 1

An Analogue of Satake Transform for p-adic Loop Groups
Proceedings of international congress of Chinese mathematicians,, Vol 2, Dec 17-22, 2007.
Zhu, Yongchang Conference paper

2006 1

On higher Frobenius-Schur indicators
Memoirs of the American Mathematical Society, No. 855, May 2006
Kashina, Y.; Sommerhauser, Y.; Zhu, Yongchang Article

2002 1

Self-dual modules of semisimple Hopf algebras
Journal of algebra, v. 257, (1), 2002, NOV 1, p. 88-96
Kashina, Y.; Sommerhauser, Y.; Zhu, YC Article

2001 3

Hecke algebras and Representation Rings of Hopf algebras
AMS/IP, Studies in Advanced Mathematics, v. 20, 2001
Zhu, Yongchang Article
On Hopf algebras with positive bases
Journal of algebra, v. 237, (2), 2001, MAR 15, p. 421-445
Lu, JH; Yan, M.; Zhu, YC Article
The dimension of irreducible modules for transitive module algebras
Communications in algebra, v. 29, (7), 2001, p. 2877-2886
Zhu, YC Article

2000 2

On the set-theoretical Yang-Baxter equation
Duke mathematical journal, v. 104, (1), 2000, JUL 15, p. 1-18
Lu, JH; Yan, M.; Zhu, YC Article
Quasi-triangular structures on Hopf algebras with positive bases
Contemporary Math., Amer. math. Soc., 2000, p. 339-356
Lu, J.; Yan, M.; Zhu, Yongchang Article

1998 1

Stabilizer for Hopf algebra actions
Communications in algebra, v. 26, (12), 1998, p. 3885-3898
Yan, M.; Zhu, YC Article

1997 1

A commuting pair in Hopf algebras
Proceedings of the American Mathematical Society, v. 125, (10), 1997, OCT, p. 2847-2851
Zhu, Y. Article

1996 1

Modular invariance of characters of vertex operator algebras
Journal of the American Mathematical Society, v. 9, (1), 1996, JAN, p. 237-302
Zhu, YC Article

1994 4

Discrete series of the Virasoro algebra and the moonshine module, In: Algebraic groups and their generalizations: quantum and infinite-dimensional methods
Sympos. Pure Math, v. 56, (2), p. 295-316, AMS 1994
Dong, C.; Mason, G.; Zhu, Yongchang Article
Global Vertex Operators on Riemann Surfaces
Communications in Math. Phys, v. 165, (3), 1994, p. 485-531
Zhu, Yongchang Article
Hopf algebras of prime dimension
Internat. Math. Res. Notices, (1), 1994, p. 53-59
Zhu, Yongchang Article
Weight spaces and root spaces of Kac-Moody algebras
J. Algebra, v. 168, (3), 1994, p. 936-948
Zhu, Yongchang Article

1992 1

Vertex operator algebras associated to representations of affine and Virasoro Algebras
Duke Mathematical Journal, v. 66, p. 123-168, 1992
Frenkel, I.; Zhu, Yongchang Article


No Publications


No Publications


No Publications






Teaching Assignment

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2021-22 Winter 0 2021-22 Fall 2 2020-21 Summer 0 2020-21 Spring 1 2020-21 Winter 0 2020-21 Fall 2

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MATH3121 Abstract Algebra
MATH6150L Introduction to Modular Forms and Automorphic Forms


MATH6170D An Introduction to Algebraic Number Theory


MATH3121 Abstract Algebra
MATH5111 Advanced Algebra I


No Teaching Assignments


No Teaching Assignments


No Teaching Assignments






Research Postgraduate (RPG) Supervision From January 2019 to December 2022 (As of 30 January 2022)

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All Supervisions Current RPGs Graduated RPGs

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Current RPGs

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Doctor of Philosophy CHEN, Yanze
Mathematics( 2017 - )

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Graduated RPGs

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Doctor of Philosophy DAI, Xuanzhong
Mathematics( Completed in 2020 )









ProjectsFrom January 2020 to December 2022

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All Projects 3

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No Projects.
Unipotent ideals and unipotent representations attached to the model orbit


模轨道对应的幂单理想和幂单表示 Leading


RGC - General Research Fund


Project Team (HKUST)
ZHU Yongchang (Lead)


2021 -




Automorphic forms on loop groups and theta lifting


圈群的自守型和 theta 提升 Leading


RGC - General Research Fund


Project Team (HKUST)
ZHU Yongchang (Lead)


2019 -




Euler-Poincaré presentation of Bernstein Projectors


伯恩斯坦投影算子的欧拉-庞加莱表示 Leading


RGC - General Research Fund


Project Team (HKUST)
ZHU Yongchang (Lead)


2019 -