Ivan Chi Ho IP
叶智皓
PhD in Mathematics
Yale University, 2012

Associate Professor
Department of Mathematics



(852) 2358 7431
ivanip@ust.hk
Room 3483
Personal Web

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Google Scholar
oZk0qlUAAAAJ

ORCID
0000-0003-4522-3374

ResearcherID
C-2898-2013

Scopus ID
55488714100




Research Interest Publications Projects Teaching Assignment RPG Supervision Space used




Research Interest

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Algebras and quantum groups
Integrable systems
Representation theory



Publications

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All Years 20 2022 0 2021 1 2020 1 2019 2 2018 3 2017 0 2016 13

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2021 1

On tensor product decomposition of positive representations of U _qq^~(sl(2, R))
Letters in Mathematical Physics, v. 111, (2), April 2021, article number 39
Ip, Ivan Chi Ho Article

2020 1

Positive Representations of Split Real Simply-Laced Quantum Groups
Publications of the Research Institute for Mathematical Sciences, v. 56, (3), 17 June 2020, p. 603-646
Ip, Ivan Chi Ho Article

2019 2

Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra
Theoretical and Mathematical Physics(Russian Federation), v. 198, (2), February 2019, p. 215-238
Ip, Ivan Chi Ho Article
On Ramond Decorations
Communications In Mathematical Physics, v. 371, (1), October 2019, p. 145-157
Ip, Ivan Chi Ho; Penner, Robert Clark; Zeitlin, Anton M. Article

2018 3

Cluster Realization of U_q(g) and Factorizations of The Universal R-matrix
Selecta Mathematica, New Series, v. 24, (5), November 2018, p. 4461-4553
Ip, Ivan Chi Ho Article
N=2 super-Teichmuller theory
Advances in Mathematics, v. 336, October 2018, p. 409-454
Ip, Ivan Chi Ho; Robert C. Penner; Anton M. Zeitlin Article
On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra U_qq (b_?)
Transactions of the American Mathematical Society, v. 370, (6), June 2018, p. 4177-4200
Ip, Ivan Chi Ho Article

2016 2

Positive Casimir and Central Characters of Split Real Quantum Groups
Communications in Mathematical Physics, v. 344, (3), June 2016, p. 857-888
Ip, Ivan Chi Ho Article
Quantum Dilogarithm Identities at Root of Unity
International Mathematics Research Notices, v. 2016, (3), 2016, p. 669-695
Ip, Ivan Chi Ho; Yamazaki, M. Article

2015 3

Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori
Journal of Pure and Applied Algebra, v. 219, (12), December 2015, p. 5650-5672
Ip, Ivan Chi Ho Article
Positive Representations of Non-simply-laced Split Real Quantum Groups
Journal of Algebra, v. 425, March 2015, p. 245-276
Ip, Ivan Chi Ho Article
Positive Representations of Split Real Quantum Groups: The Universal R Operator
International Mathematics Research Notices, v. 2015, (1), 2015, p. 240-287
Ip, Ivan Chi Ho Article

2014 5

Positive Representations of Split Real Quantum Groups and Future Perspectives
International Mathematics Research Notices, v. 2014, (8), January 2014, p. 2126-2164
Frenkel, I.B.; Ip, Ivan Chi Ho Article
Q-Operator and Fusion Relations for U_q(C⁽²⁾(2))
Letters in Mathematical Physics, v. 104, (8), July 2014, p. 1019-1043
Ip, Ivan Chi Ho; Zeitlin, A.M. Article
Supersymmetry and the Modular Double
Contemporary Mathematics, v. 623, 2014, p. 81-91
Ip, Ivan Chi Ho; Zeitlin, Anton M Article
On the work of Igor Frenkel
Contemporary Mathematics, v. 610, 2014, p. 1-21
Duncan, John; Etingof, Pavel; Ip, Ivan Chi Ho; Khovanov, Mikhail; Libine, Matvei; Licata, Anthony; Savage, Alistair; Schlosser, Michael Conference paper
Positive Representations, Multiplier Hopf Algebra, and Continuous Canonical Basis
2013 RIMS symposium on String theory, integrable systems and representation theory, Kyoto, Japan, 30 July - 2 August 2013
Ip, Ivan Chi Ho Conference paper

2013 2

Representation of the Quantum Plane, Its Quantum Double, and Harmonic Analysis on GL_q⁺(2, ?)
Selecta Mathematica, New Series, v. 19, (4), November 2013, p. 987-1082
Ip, Ivan Chi Ho Article
The Classical Limit of Representation Theory of the Quantum Plane
International Journal of Mathematics, v. 24, (4), April 2013, article number 1350031
Ip, Ivan Chi Ho Article

2012 1

Positive Representations of Split Real Quantum Groups
Nankai Series in Pure, Applied Mathematics and Theoretical Physics: Symmetries and Groups in Contemporary Physics, v. 11, 2012, p. 175-180
Ip, Ivan Chi Ho Conference paper


Expand All Collapse All


Article 1

On tensor product decomposition of positive representations of U _qq^~(sl(2, R))
Letters in Mathematical Physics, v. 111, (2), April 2021, article number 39
Ip, Ivan Chi Ho


Expand All Collapse All


Article 1

Positive Representations of Split Real Simply-Laced Quantum Groups
Publications of the Research Institute for Mathematical Sciences, v. 56, (3), 17 June 2020, p. 603-646
Ip, Ivan Chi Ho


Expand All Collapse All


Article 2

Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra
Theoretical and Mathematical Physics(Russian Federation), v. 198, (2), February 2019, p. 215-238
Ip, Ivan Chi Ho
On Ramond Decorations
Communications In Mathematical Physics, v. 371, (1), October 2019, p. 145-157
Ip, Ivan Chi Ho; Penner, Robert Clark; Zeitlin, Anton M.


Expand All Collapse All


Article 3

Cluster Realization of U_q(g) and Factorizations of The Universal R-matrix
Selecta Mathematica, New Series, v. 24, (5), November 2018, p. 4461-4553
Ip, Ivan Chi Ho
N=2 super-Teichmuller theory
Advances in Mathematics, v. 336, October 2018, p. 409-454
Ip, Ivan Chi Ho; Robert C. Penner; Anton M. Zeitlin
On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra U_qq (b_?)
Transactions of the American Mathematical Society, v. 370, (6), June 2018, p. 4177-4200
Ip, Ivan Chi Ho


Expand All Collapse All


Article 2

Positive Casimir and Central Characters of Split Real Quantum Groups
Communications in Mathematical Physics, v. 344, (3), June 2016, p. 857-888
Ip, Ivan Chi Ho
Quantum Dilogarithm Identities at Root of Unity
International Mathematics Research Notices, v. 2016, (3), 2016, p. 669-695
Ip, Ivan Chi Ho; Yamazaki, M.


Expand All Collapse All


Article 3

Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori
Journal of Pure and Applied Algebra, v. 219, (12), December 2015, p. 5650-5672
Ip, Ivan Chi Ho
Positive Representations of Non-simply-laced Split Real Quantum Groups
Journal of Algebra, v. 425, March 2015, p. 245-276
Ip, Ivan Chi Ho
Positive Representations of Split Real Quantum Groups: The Universal R Operator
International Mathematics Research Notices, v. 2015, (1), 2015, p. 240-287
Ip, Ivan Chi Ho


Expand All Collapse All


Article 3

Positive Representations of Split Real Quantum Groups and Future Perspectives
International Mathematics Research Notices, v. 2014, (8), January 2014, p. 2126-2164
Frenkel, I.B.; Ip, Ivan Chi Ho
Q-Operator and Fusion Relations for U_q(C⁽²⁾(2))
Letters in Mathematical Physics, v. 104, (8), July 2014, p. 1019-1043
Ip, Ivan Chi Ho; Zeitlin, A.M.
Supersymmetry and the Modular Double
Contemporary Mathematics, v. 623, 2014, p. 81-91
Ip, Ivan Chi Ho; Zeitlin, Anton M

Conference paper 2

On the work of Igor Frenkel
Contemporary Mathematics, v. 610, 2014, p. 1-21
Duncan, John; Etingof, Pavel; Ip, Ivan Chi Ho; Khovanov, Mikhail; Libine, Matvei; Licata, Anthony; Savage, Alistair; Schlosser, Michael
Positive Representations, Multiplier Hopf Algebra, and Continuous Canonical Basis
2013 RIMS symposium on String theory, integrable systems and representation theory, Kyoto, Japan, 30 July - 2 August 2013
Ip, Ivan Chi Ho


Expand All Collapse All


Article 2

Representation of the Quantum Plane, Its Quantum Double, and Harmonic Analysis on GL_q⁺(2, ?)
Selecta Mathematica, New Series, v. 19, (4), November 2013, p. 987-1082
Ip, Ivan Chi Ho
The Classical Limit of Representation Theory of the Quantum Plane
International Journal of Mathematics, v. 24, (4), April 2013, article number 1350031
Ip, Ivan Chi Ho


Expand All Collapse All


Conference paper 1

Positive Representations of Split Real Quantum Groups
Nankai Series in Pure, Applied Mathematics and Theoretical Physics: Symmetries and Groups in Contemporary Physics, v. 11, 2012, p. 175-180
Ip, Ivan Chi Ho


Expand All Collapse All


2016 2

Positive Casimir and Central Characters of Split Real Quantum Groups
Communications in Mathematical Physics, v. 344, (3), June 2016, p. 857-888
Ip, Ivan Chi Ho Article
Quantum Dilogarithm Identities at Root of Unity
International Mathematics Research Notices, v. 2016, (3), 2016, p. 669-695
Ip, Ivan Chi Ho; Yamazaki, M. Article

2015 3

Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori
Journal of Pure and Applied Algebra, v. 219, (12), December 2015, p. 5650-5672
Ip, Ivan Chi Ho Article
Positive Representations of Non-simply-laced Split Real Quantum Groups
Journal of Algebra, v. 425, March 2015, p. 245-276
Ip, Ivan Chi Ho Article
Positive Representations of Split Real Quantum Groups: The Universal R Operator
International Mathematics Research Notices, v. 2015, (1), 2015, p. 240-287
Ip, Ivan Chi Ho Article

2014 5

Positive Representations of Split Real Quantum Groups and Future Perspectives
International Mathematics Research Notices, v. 2014, (8), January 2014, p. 2126-2164
Frenkel, I.B.; Ip, Ivan Chi Ho Article
Q-Operator and Fusion Relations for U_q(C⁽²⁾(2))
Letters in Mathematical Physics, v. 104, (8), July 2014, p. 1019-1043
Ip, Ivan Chi Ho; Zeitlin, A.M. Article
Supersymmetry and the Modular Double
Contemporary Mathematics, v. 623, 2014, p. 81-91
Ip, Ivan Chi Ho; Zeitlin, Anton M Article
On the work of Igor Frenkel
Contemporary Mathematics, v. 610, 2014, p. 1-21
Duncan, John; Etingof, Pavel; Ip, Ivan Chi Ho; Khovanov, Mikhail; Libine, Matvei; Licata, Anthony; Savage, Alistair; Schlosser, Michael Conference paper
Positive Representations, Multiplier Hopf Algebra, and Continuous Canonical Basis
2013 RIMS symposium on String theory, integrable systems and representation theory, Kyoto, Japan, 30 July - 2 August 2013
Ip, Ivan Chi Ho Conference paper

2013 2

Representation of the Quantum Plane, Its Quantum Double, and Harmonic Analysis on GL_q⁺(2, ?)
Selecta Mathematica, New Series, v. 19, (4), November 2013, p. 987-1082
Ip, Ivan Chi Ho Article
The Classical Limit of Representation Theory of the Quantum Plane
International Journal of Mathematics, v. 24, (4), April 2013, article number 1350031
Ip, Ivan Chi Ho Article

2012 1

Positive Representations of Split Real Quantum Groups
Nankai Series in Pure, Applied Mathematics and Theoretical Physics: Symmetries and Groups in Contemporary Physics, v. 11, 2012, p. 175-180
Ip, Ivan Chi Ho Conference paper


No Publications


No Publications






Teaching Assignment

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2021-22 Winter 0 2021-22 Fall 6 2020-21 Summer 2 2020-21 Spring 6 2020-21 Winter 0 2020-21 Fall 4

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MATH3043 Honors Real Analysis
MATH5111 Advanced Algebra I
MATH6913P Reading Course: Quiver Representations and Quiver Varieties
SCIE3500 IRE Research Project I
SCIE4500 IRE Research Project II
UROP2100E Undergraduate Research Opportunities Series 2


UROP1100D Undergraduate Research Opportunities Series 1
UROP2100D Undergraduate Research Opportunities Series 2


MATH2023 Multivariable Calculus
MATH2043 Honors Mathematical Analysis
MATH4991 Capstone Project in Pure Mathematics
SCIE1500 Guided Study on Research I
SCIE2500 Guided Study on Research II
SCIE3500 IRE Research Project I


MATH2131 Honors in Linear and Abstract Algebra I
MATH4999 Independent Capstone Project
SCIE3500 IRE Research Project I
SCIE4500 IRE Research Project II


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 GAO, Kailong
Mathematics( 2020 - )

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Master of Philosophy CHOY, Ka Hei
Mathematics( 2021 - )

LI, Yunhe
Mathematics( 2021 - )

YE, Jeff York
Mathematics( 2021 - )

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Graduated RPGs

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Master of Philosophy WONG, Chun Wai
Mathematics( Completed in 2021 )

SO, Chi Long Ivan
Mathematics( Completed in 2020 )









ProjectsFrom January 2020 to December 2022

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All Projects 2

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No Projects.
The Theory of Positive Representations and Its Applications


正表示论及其应用 Leading


RGC - Early Career Scheme


Project Team (HKUST)
IP Ivan Chi Ho (Lead)


2020 -




Quantum Parallel Transport of Positive Representations Leading


Central Reserve Fund - School-based Initiatives


Project Team (HKUST)
IP Ivan Chi Ho (Lead)


2019 - 2021