Professor Ruibin Zhang

F07 - Carslaw Building
The University of Sydney

Telephone 9351 3444
Fax 9351 4534

Website Personal web page

Research interests

  • Lie Theory
  • Representation Theory
  • Supersymmetry
  • Quantum Field Theory
  • Ruibin Zhang is a member of the Algebra Research Group.

Teaching and supervision

Timetable

PhD and master's project opportunities

Selected grants

2012

  • Quantised algebras, supersymmetry and invariant theory; Lehrer G, Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2009

  • Noncommutative geometry in representation theory and quantum physics; Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).
  • Topological Problems in Quantum Field Theory; Liu X, Zhang R; DVC Research/Postdoctoral Research Fellowship Scheme.

2007

  • Invariant theory, cellularity and geometry.; Lehrer G, Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2006

  • Infinite dimensional unitarizable representations of Lie superalgearas; Zhang R, Molev A; Australian Research Council (ARC)/Discovery Projects (DP).

2004

  • Geometry & representations of classical & quantum Lie supergroups; Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2002

  • Representations and Applications of Quantum Groups; Zhang R, Molev A; Australian Research Council (ARC)/Discovery Projects (DP).
  • Not known; Zhang R; DVC Research/Research and Development Scheme: Research and Development (R&D).

2001

  • Quantum superalgebras, Yangians and their applications; Zhang R; DVC Research/Bridging Support Grant.

2000

  • ARC Senior Research Fellowship F69802444 commenced 16.12.98 University of Queensland, transferred to University of Sydney to commence on 16.1.2000; Australian Research Council (ARC)/Australian Senior Research Fellowship.
  • Quantum and classical Lie Supergroups; Zhang R; Australian Research Council (ARC)/Small Grants.

1999

  • Vassiliev invariants and quantum superalgebras; Zhang R; Australian Research Council (ARC)/Small Grants.

Selected publications

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Book Chapters

  • Lehrer, G., Zhang, R. (2010). A Temperley-Lieb Analogue for the BMW Algebra. In A Gyoja, H Nakajima, K Shinoda, T Shoji, T Tanisaki (Eds.), Representation Theory of Algebraic Groups and Quantum Groups, (pp. 155-190). New York: Birkhauser (imprint of Springer).

Journals

  • Xia, C., Zhang, R. (2013). Unitary highest weight modules over block type lie algebras B(q). Journal of Lie Theory, 23(1), 159-176.
  • Chaichian, M., Tureanu, A., Zhang, R. (2012). Extended PoincarĂ© supersymmetry in three dimensions and supersymmetric anyons. Journal of Mathematical Physics, 53(7), 1-8. [More Information]
  • Su, Y., Zhang, R. (2012). Generalised Jantzen filtration of Lie superalgebras I. European Mathematical Society Journal, 14(4), 1103-1133. [More Information]
  • Su, Y., Zhang, R. (2012). Generalised Verma modules for the orthosymplectic Lie superalgebra ospk|2. Journal of Algebra, 357, 94-115. [More Information]
  • Coulembier, K., Zhang, R. (2012). Invariant integration on orthosymplectic and unitary supergroups. Journal of Physics A: Mathematical and Theoretical, 45(2012), 1-32. [More Information]
  • Lehrer, G., Zhang, R. (2012). Quantum group actions on rings and equivariant K-theory. Contemporary Mathematics, 565, 115-141.
  • Lehrer, G., Zhang, R. (2012). The second fundamental theorem of invariant theory for the orthogonal group. Annals of Mathematics, 176(3), 2031-2054. [More Information]
  • Lehrer, G., Zhang, H., Zhang, R. (2011). A Quantum Analogue of the First Fundamental Theorem of Classical Invariant Theory. Communications in Mathematical Physics, 301, 131-174. [More Information]
  • Lehrer, G., Nakano, D., Zhang, R. (2011). Detecting cohomology for Lie superalgebras. Advances in Mathematics, 228(4), 2098-2115. [More Information]
  • Meng, G., Zhang, R. (2011). Generalized MICZ-Kepler problems and unitary highest weight modules. Journal of Mathematical Physics, 52(4), 042106-1-042106-23. [More Information]
  • Lam, N., Zhang, R. (2011). u-Cohomology formula for unitarizable modules over general linear superalgebras. Journal of Algebra, 327(1), 50-70. [More Information]
  • Sun, W., Wang, D., Xie, N., Zhang, R., Zhang, X. (2010). Gravitational collapse of spherically symmetric stars in noncommutative general relativity. European Physical Journal C. Particles and Fields, 69, 271-279. [More Information]
  • Zhang, R., Zhang, X. (2010). Projective module description of embedded noncommutative spaces. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 22(5), 507-531.
  • Ke, W., Lai, K., Zhang, R. (2010). Quantum codes from Hadamard matrices. Linear and Multilinear Algebra, 58(7), 847-854. [More Information]
  • Liu, X., Zhang, R. (2010). Topological vortices in chiral gauge theory of graphene. Annals of Physics, 325, 384-391. [More Information]
  • Wang, D., Zhang, R., Zhang, X. (2009). Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves. The European Physical Journal - Applied Physics, 64, 439-444.
  • Wang, D., Zhang, R., Zhang, X. (2009). Quantum deformations of Schwarzschild and Schwarzchild-de Sitter spacetimes. Classical and Quantum Gravity, 26(8), 085014-1-085014-14.
  • Wu, Y., Zhang, R. (2009). Unitary highest weight representations of quantum general linear superalgebra. Journal of Algebra, 321(11), 3568-3593. [More Information]
  • Billig, Y., Molev, A., Zhang, R. (2008). Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus. Advances in Mathematics, 218(6), 1972-2004. [More Information]
  • Zhang, G., Zhang, R. (2008). Equivariant vector bundles on quantum homogeneous spaces. Mathematical Research Letters, 15(2), 297-307.
  • Chaichian, M., Kulish, P., Tureanu, A., Zhang, R., Zhang, X. (2008). Noncommutative fields and actions of twisted Poincare algebra. Journal of Mathematical Physics, 49, 042302-1-042302-16. [More Information]
  • Lehrer, G., Zhang, R. (2008). On Endomorphisms of Quantum Tensor Space. Letters in Mathematical Physics, 86, 209-227. [More Information]
  • Zhang, R. (2008). Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems. Communications in Mathematical Physics, 280(2), 545-562. [More Information]
  • Chaichian, M., Tureanu, A., Zhang, R., Zhang, X. (2008). Riemannian geometry of noncommutative surfaces. Journal of Mathematical Physics, 49(7), 073511-1-073511-26.
  • Cheng, S., Wang, W., Zhang, R. (2008). Super duality and Kazhdan-Lusztig polynomials. Transactions of the American Mathematical Society, 360(11), 5883-5924.
  • Cheng, S., Wang, W., Zhang, R. (2007). A Fock space approach to representation theory of osp(2/2n). Transformation Groups, 12(2), 209-225. [More Information]
  • Su, Y., Zhang, R. (2007). Character and dimension formulae for general linear superalgebra. Advances in Mathematics, 211(1), 1-33. [More Information]
  • Su, Y., Zhang, R. (2007). Cohomology of Lie Superalgebras slm\n and osp2\2n. Proceedings of the London Mathematical Society, 94(1), 91-136. [More Information]
  • Zhang, H., Zhang, R. (2006). Dual canonical bases for the quantum general linear supergroup. Journal of Algebra, 304(2), 1026-1058. [More Information]
  • Chebotar, M., Ke, W., Lee, P., Zhang, R. (2006). On maps preserving zero Jordan products. Monatshefte fur Mathematik, 149(2), 91-101. [More Information]
  • Lehrer, G., Zhang, R. (2006). Strongly multiplicity free modules for Lie algebras and quantum groups. Journal of Algebra, 306(1), 138-174. [More Information]
  • Zhang, H., Zhang, R. (2005). Dual canonical bases for the quantum special linear group and invariant subalgebras. Letters in Mathematical Physics, 73(3), 165-181. [More Information]
  • Scheunert, M., Zhang, R. (2005). Integration on Lie supergroups: A Hopf superalgebra approach. Journal of Algebra, 292(2), 324-342. [More Information]
  • Dobrev, V., Zhang, R. (2005). Positive energy unitary irreducible representations of the superalgebras osp(1|2n, R). Physics of Atomic Nuclei, 68(10), 1660-1669.
  • Lam, N., Zhang, R. (2005). Quasi-finite modules for Lie superalgebras of infinite rank. Transactions of the American Mathematical Society, 358(1), 403-439.
  • Jarvis, P., Zhang, R. (2005). Resolution of the GL(3) superset of O(3) state labelling problem via the O(3)-invariant Bethe subalgebra of the twisted Yangian. Journal of Physics A: Mathematical and General, 38(14), L219-L226.
  • Zhang, R., Zou, Y. (2005). Spherical functions on homogeneous superspaces. Journal of Mathematical Physics, 46(4), 043513-1-043513-21.
  • Cheng, S., Zhang, R. (2004). Analogue Of Kostant's U-Cohomology Formula For The General Linear Superalgebra. International Mathematics Research Notices, 2004 (1), 31-53.
  • Cheng, S., Lam, N., Zhang, R. (2004). Character Formula For Infinite-Dimensional Unitarizable Modules Of The General Linear Superalgebra. Journal of Algebra, 273(2), 780-805.
  • Cheng, S., Zhang, R. (2004). Howe Duality And Combinatorial Character Formula For Orthosymplectic Lie Superalgebras. Advances in Mathematics, 182(1), 124-172.
  • Molev, A., Tolstoy, V., Zhang, R. (2004). On Irreducibility Of Tensor Products Of Evaluation Modules For The Quantum Affine Algebra. Journal of Physics A: Mathematical and General, 37(6), 2385-2399.
  • Zhang, R. (2004). Quantum Superalgebra Representations On Cohomology Groups Of Non-Commutative Bundles. Journal of Pure and Applied Algebra, 191(3), 285-314.
  • Zhang, R. (2003). Howe duality and the quantum general linear group. Proceedings of the American Mathematical Society, 131(9), 2681-2692.
  • Lai, K., Zhang, R. (2003). Multiplicity Free Actions of Quantum Groups and Generalized Howe Duality. Letters in Mathematical Physics, 64(3), 255-272.
  • Zhang, R. (2002). Quantum enveloping superalgebras and link invariants. Journal of Mathematical Physics, 43(4), 2029-2048.
  • Scheunert, M., Zhang, R. (2002). The general linear supergroup and its Hopf superalgebra of regular functions. Journal of Algebra, 254(1), 44-83.
  • Scheunert, M., Zhang, R. (2001). Invariant integration on classical and quantum Lie supergroups. Journal of Mathematical Physics, 42(8), 3871-3897.

2013

  • Xia, C., Zhang, R. (2013). Unitary highest weight modules over block type lie algebras B(q). Journal of Lie Theory, 23(1), 159-176.

2012

  • Chaichian, M., Tureanu, A., Zhang, R. (2012). Extended PoincarĂ© supersymmetry in three dimensions and supersymmetric anyons. Journal of Mathematical Physics, 53(7), 1-8. [More Information]
  • Su, Y., Zhang, R. (2012). Generalised Jantzen filtration of Lie superalgebras I. European Mathematical Society Journal, 14(4), 1103-1133. [More Information]
  • Su, Y., Zhang, R. (2012). Generalised Verma modules for the orthosymplectic Lie superalgebra ospk|2. Journal of Algebra, 357, 94-115. [More Information]
  • Coulembier, K., Zhang, R. (2012). Invariant integration on orthosymplectic and unitary supergroups. Journal of Physics A: Mathematical and Theoretical, 45(2012), 1-32. [More Information]
  • Lehrer, G., Zhang, R. (2012). Quantum group actions on rings and equivariant K-theory. Contemporary Mathematics, 565, 115-141.
  • Lehrer, G., Zhang, R. (2012). The second fundamental theorem of invariant theory for the orthogonal group. Annals of Mathematics, 176(3), 2031-2054. [More Information]

2011

  • Lehrer, G., Zhang, H., Zhang, R. (2011). A Quantum Analogue of the First Fundamental Theorem of Classical Invariant Theory. Communications in Mathematical Physics, 301, 131-174. [More Information]
  • Lehrer, G., Nakano, D., Zhang, R. (2011). Detecting cohomology for Lie superalgebras. Advances in Mathematics, 228(4), 2098-2115. [More Information]
  • Meng, G., Zhang, R. (2011). Generalized MICZ-Kepler problems and unitary highest weight modules. Journal of Mathematical Physics, 52(4), 042106-1-042106-23. [More Information]
  • Lam, N., Zhang, R. (2011). u-Cohomology formula for unitarizable modules over general linear superalgebras. Journal of Algebra, 327(1), 50-70. [More Information]

2010

  • Lehrer, G., Zhang, R. (2010). A Temperley-Lieb Analogue for the BMW Algebra. In A Gyoja, H Nakajima, K Shinoda, T Shoji, T Tanisaki (Eds.), Representation Theory of Algebraic Groups and Quantum Groups, (pp. 155-190). New York: Birkhauser (imprint of Springer).
  • Sun, W., Wang, D., Xie, N., Zhang, R., Zhang, X. (2010). Gravitational collapse of spherically symmetric stars in noncommutative general relativity. European Physical Journal C. Particles and Fields, 69, 271-279. [More Information]
  • Zhang, R., Zhang, X. (2010). Projective module description of embedded noncommutative spaces. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 22(5), 507-531.
  • Ke, W., Lai, K., Zhang, R. (2010). Quantum codes from Hadamard matrices. Linear and Multilinear Algebra, 58(7), 847-854. [More Information]
  • Liu, X., Zhang, R. (2010). Topological vortices in chiral gauge theory of graphene. Annals of Physics, 325, 384-391. [More Information]

2009

  • Wang, D., Zhang, R., Zhang, X. (2009). Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves. The European Physical Journal - Applied Physics, 64, 439-444.
  • Wang, D., Zhang, R., Zhang, X. (2009). Quantum deformations of Schwarzschild and Schwarzchild-de Sitter spacetimes. Classical and Quantum Gravity, 26(8), 085014-1-085014-14.
  • Wu, Y., Zhang, R. (2009). Unitary highest weight representations of quantum general linear superalgebra. Journal of Algebra, 321(11), 3568-3593. [More Information]

2008

  • Billig, Y., Molev, A., Zhang, R. (2008). Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus. Advances in Mathematics, 218(6), 1972-2004. [More Information]
  • Zhang, G., Zhang, R. (2008). Equivariant vector bundles on quantum homogeneous spaces. Mathematical Research Letters, 15(2), 297-307.
  • Chaichian, M., Kulish, P., Tureanu, A., Zhang, R., Zhang, X. (2008). Noncommutative fields and actions of twisted Poincare algebra. Journal of Mathematical Physics, 49, 042302-1-042302-16. [More Information]
  • Lehrer, G., Zhang, R. (2008). On Endomorphisms of Quantum Tensor Space. Letters in Mathematical Physics, 86, 209-227. [More Information]
  • Zhang, R. (2008). Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems. Communications in Mathematical Physics, 280(2), 545-562. [More Information]
  • Chaichian, M., Tureanu, A., Zhang, R., Zhang, X. (2008). Riemannian geometry of noncommutative surfaces. Journal of Mathematical Physics, 49(7), 073511-1-073511-26.
  • Cheng, S., Wang, W., Zhang, R. (2008). Super duality and Kazhdan-Lusztig polynomials. Transactions of the American Mathematical Society, 360(11), 5883-5924.

2007

  • Cheng, S., Wang, W., Zhang, R. (2007). A Fock space approach to representation theory of osp(2/2n). Transformation Groups, 12(2), 209-225. [More Information]
  • Su, Y., Zhang, R. (2007). Character and dimension formulae for general linear superalgebra. Advances in Mathematics, 211(1), 1-33. [More Information]
  • Su, Y., Zhang, R. (2007). Cohomology of Lie Superalgebras slm\n and osp2\2n. Proceedings of the London Mathematical Society, 94(1), 91-136. [More Information]

2006

  • Zhang, H., Zhang, R. (2006). Dual canonical bases for the quantum general linear supergroup. Journal of Algebra, 304(2), 1026-1058. [More Information]
  • Chebotar, M., Ke, W., Lee, P., Zhang, R. (2006). On maps preserving zero Jordan products. Monatshefte fur Mathematik, 149(2), 91-101. [More Information]
  • Lehrer, G., Zhang, R. (2006). Strongly multiplicity free modules for Lie algebras and quantum groups. Journal of Algebra, 306(1), 138-174. [More Information]

2005

  • Zhang, H., Zhang, R. (2005). Dual canonical bases for the quantum special linear group and invariant subalgebras. Letters in Mathematical Physics, 73(3), 165-181. [More Information]
  • Scheunert, M., Zhang, R. (2005). Integration on Lie supergroups: A Hopf superalgebra approach. Journal of Algebra, 292(2), 324-342. [More Information]
  • Dobrev, V., Zhang, R. (2005). Positive energy unitary irreducible representations of the superalgebras osp(1|2n, R). Physics of Atomic Nuclei, 68(10), 1660-1669.
  • Lam, N., Zhang, R. (2005). Quasi-finite modules for Lie superalgebras of infinite rank. Transactions of the American Mathematical Society, 358(1), 403-439.
  • Jarvis, P., Zhang, R. (2005). Resolution of the GL(3) superset of O(3) state labelling problem via the O(3)-invariant Bethe subalgebra of the twisted Yangian. Journal of Physics A: Mathematical and General, 38(14), L219-L226.
  • Zhang, R., Zou, Y. (2005). Spherical functions on homogeneous superspaces. Journal of Mathematical Physics, 46(4), 043513-1-043513-21.

2004

  • Cheng, S., Zhang, R. (2004). Analogue Of Kostant's U-Cohomology Formula For The General Linear Superalgebra. International Mathematics Research Notices, 2004 (1), 31-53.
  • Cheng, S., Lam, N., Zhang, R. (2004). Character Formula For Infinite-Dimensional Unitarizable Modules Of The General Linear Superalgebra. Journal of Algebra, 273(2), 780-805.
  • Cheng, S., Zhang, R. (2004). Howe Duality And Combinatorial Character Formula For Orthosymplectic Lie Superalgebras. Advances in Mathematics, 182(1), 124-172.
  • Molev, A., Tolstoy, V., Zhang, R. (2004). On Irreducibility Of Tensor Products Of Evaluation Modules For The Quantum Affine Algebra. Journal of Physics A: Mathematical and General, 37(6), 2385-2399.
  • Zhang, R. (2004). Quantum Superalgebra Representations On Cohomology Groups Of Non-Commutative Bundles. Journal of Pure and Applied Algebra, 191(3), 285-314.

2003

  • Zhang, R. (2003). Howe duality and the quantum general linear group. Proceedings of the American Mathematical Society, 131(9), 2681-2692.
  • Lai, K., Zhang, R. (2003). Multiplicity Free Actions of Quantum Groups and Generalized Howe Duality. Letters in Mathematical Physics, 64(3), 255-272.

2002

  • Zhang, R. (2002). Quantum enveloping superalgebras and link invariants. Journal of Mathematical Physics, 43(4), 2029-2048.
  • Scheunert, M., Zhang, R. (2002). The general linear supergroup and its Hopf superalgebra of regular functions. Journal of Algebra, 254(1), 44-83.

2001

  • Scheunert, M., Zhang, R. (2001). Invariant integration on classical and quantum Lie supergroups. Journal of Mathematical Physics, 42(8), 3871-3897.

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