Professor Alexander Molev

F07 - Carslaw Building
The University of Sydney

Telephone 9351 5793
Fax 9351 4534

Research interests

  • Classical Lie algebras and their representations
  • Affine Kac-Moody algebras
  • Quantum groups
  • Algebraic combinatorics

List of publications

Talks and lectures

Teaching and supervision

Postgraduate students

Timetable

Awards and honours

2001: Medal of the Australian Mathematical Society

Selected grants

2014

  • Affine Lie algebras at the critical level; Molev A; DVC Research/Bridging Support Grant.

2011

  • Vertex algebras and representations of quantum groups; Molev A; Australian Research Council (ARC)/Discovery Projects (DP).

2008

  • Quantum algebras: their symmetries, invariants and representations; Molev A; 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).

2002

  • Representations and Applications of Quantum Groups; Zhang R, Molev A; Australian Research Council (ARC)/Discovery Projects (DP).

2000

  • Capelli identities for classical Lie superalgebras.; Molev A; Australian Research Council (ARC)/Small Grants.

Selected publications

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Books

  • Molev, A. (2007). Yangians and Classical Lie Algebras. Providence, RI, USA: American Mathematical Society.

Book Chapters

  • Molev, A. (2006). Gelfand-Tsetlin bases for classical Lie algebras. In M. Hazewinkel (Eds.), Handbook of algebra. Vol 4, (pp. 109-170). Amsterdam ; New York: Elsevier.
  • Molev, A. (2003). Yangians and their applications. In M. Hazelwinkel (Eds.), Handbook of Algebra. Vol 3, (pp. 909-959). Amsterdam ; London: Elsevier.

Journals

  • Molev, A., Ragoucy, E. (2014). The MacMahon Master Theorem for Right Quantum Superalgebras and Higher Sugawara Operators for gl(m|n). Moscow Mathematical Journal, 14(1), 83-119.
  • Iorgov, N., Molev, A., Ragoucy, E. (2013). Casimir elements from the Brauer-Schur-Weyl duality. Journal of Algebra, 387, 144-159. [More Information]
  • Molev, A., Rozhkovskaya, N. (2013). Characteristic maps for the Brauer algebra. Journal of Algebraic Combinatorics, 38(1), 15-35. [More Information]
  • Molev, A. (2013). Feigin-Frenkel center in types B, C and D. Inventiones Mathematicae, 191(1), 1-34. [More Information]
  • Isaev, A., Molev, A., Ogievetesky, O. (2012). A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms. International Mathematics Research Notices, 2012 (11), 2571-2606. [More Information]
  • Davydov, A., Molev, A. (2011). A categorical approach to classical and quantum Schur-Weyl duality. Contemporary Mathematics, 537, 143-171.
  • Molev, A. (2011). Combinatorial Bases For Covariant Representations Of The Lie Superalgebra math symbols gl(m/n). Academia Sinica. Institute of Mathematics. Bulletin, 6(4), 415-462.
  • Isaev, A., Molev, A. (2010). Fusion procedure for the Brauer algebra. Algebra i Analiz, 22(3), 142-154.
  • Gow, L., Molev, A. (2010). Representations of twisted q-Yangians. Selecta Mathematica - New Series, 16(3), 439-499. [More Information]
  • Molev, A. (2009). Comultiplication rules for the double Schur functions and Cauchy identities. The Journal of Combinatorics, 16(1), R13-1-R13-44.
  • Molev, A. (2009). Littlewood-Richardson polynomials. Journal of Algebra, 321(11), 3450-3468. [More Information]
  • Chervov, A., Molev, A. (2009). On higher-order Sugawara operators. International Mathematics Research Notices, 2009 (9), 1612-1635. [More Information]
  • Futorny, V., Molev, A., Ovsienko, S. (2009). The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras. Advances in Mathematics, 223(3), 773-796. [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]
  • Molev, A. (2008). On the fusion procedure for the symmetric group. Reports on Mathematical Physics, 61(2), 181-188.
  • Isaev, A., Molev, A., Os'Kin, A. (2008). On the Idempotents of Hecke Algebras. Letters in Mathematical Physics, 85(1), 79-90. [More Information]
  • Molev, A., Ragoucy, E. (2008). Symmetries and invariants of twisted quantum algebras and associated Poisson algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 20(2), 173-198.
  • Hopkins, M., Molev, A. (2006). A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2, 092-1-092-29.
  • Arnaudon, D., Molev, A., Ragoucy, E. (2006). On the R-Matrix Realization of Yangians and their Representations. Annales Henri Poincare, 7, 1269-1325. [More Information]
  • Hopkins, M., Molev, A. (2006). On the skew representations of the quantum affine algebra. Czechoslovak Journal of Physics: europhysics journal, 56(10/11), 1179-1184. [More Information]
  • Molev, A. (2006). Representations of the twisted quantized enveloping algebra of type Cn. Moscow Mathematical Journal, 6(3), 531-551.
  • Molev, A. (2006). Skew representations of twisted Yangians. Selecta Mathematica - New Series, 12(1), 1-38. [More Information]
  • Billig, Y., Futorny, V., Molev, A. (2006). Verma modules for Yangians. Letters in Mathematical Physics, 78(1), 1-16. [More Information]
  • Futorny, V., Molev, A., Ovsienko, S. (2005). Harish-Chandra modules for Yangians. Representation Theory, 9, 426-454.
  • Bahturin, Y., Molev, A. (2004). Casimir elements for some graded Lie algebras and superalgebras. Czechoslovak Journal of Physics: europhysics journal, 54(11), 1159-1164. [More Information]
  • 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.
  • Molev, A., Retakh, V. (2004). Quasideterminants And Casimir Elements For The General Linear Lie Superalgebra. International Mathematics Research Notices, 2004 (13), 611-619.
  • Molev, A. (2004). The 8th Problem: Littlewood-Richardson problem for Schubert polynomials. Gazette of the Australian Mathematical Society, 31(5), 295-297.
  • Molev, A. (2003). A new quantum analog of the Brauer algebra. Czechoslovak Journal of Physics: europhysics journal, 53(11), 1073-1078.
  • Molev, A., Ragoucy, E., Sorba, P. (2003). Coideal subalgebras in quantum affine algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 1(1), 789-822.
  • Molev, A. (2002). Irreducibility criterion for tensor products of Yangian evaluation modules. Duke Mathematical Journal, 112(2), 307-341.
  • Molev, A., Ragoucy, E. (2002). Representations of reflection algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 14(3), 317-342.
  • Molev, A. (2002). Yangians and transvector algebras. Discrete Mathematics, 246(1), 231-253.
  • Molev, A., Olshanski, G. (2001). Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Journal of Algebra, 237(1), 302-341.

Conferences

  • Futorny, V., Molev, A., Ovsienko, S. (2008). Gelfand-Tsetlin Bases for Representations of Finite W-Algebras and Shifted Yangians. VII International Workshop Lie theory and its applications in physics, Sofia, Bulgaria: Heron Publishing.

2014

  • Molev, A., Ragoucy, E. (2014). The MacMahon Master Theorem for Right Quantum Superalgebras and Higher Sugawara Operators for gl(m|n). Moscow Mathematical Journal, 14(1), 83-119.

2013

  • Iorgov, N., Molev, A., Ragoucy, E. (2013). Casimir elements from the Brauer-Schur-Weyl duality. Journal of Algebra, 387, 144-159. [More Information]
  • Molev, A., Rozhkovskaya, N. (2013). Characteristic maps for the Brauer algebra. Journal of Algebraic Combinatorics, 38(1), 15-35. [More Information]
  • Molev, A. (2013). Feigin-Frenkel center in types B, C and D. Inventiones Mathematicae, 191(1), 1-34. [More Information]

2012

  • Isaev, A., Molev, A., Ogievetesky, O. (2012). A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms. International Mathematics Research Notices, 2012 (11), 2571-2606. [More Information]

2011

  • Davydov, A., Molev, A. (2011). A categorical approach to classical and quantum Schur-Weyl duality. Contemporary Mathematics, 537, 143-171.
  • Molev, A. (2011). Combinatorial Bases For Covariant Representations Of The Lie Superalgebra math symbols gl(m/n). Academia Sinica. Institute of Mathematics. Bulletin, 6(4), 415-462.

2010

  • Isaev, A., Molev, A. (2010). Fusion procedure for the Brauer algebra. Algebra i Analiz, 22(3), 142-154.
  • Gow, L., Molev, A. (2010). Representations of twisted q-Yangians. Selecta Mathematica - New Series, 16(3), 439-499. [More Information]

2009

  • Molev, A. (2009). Comultiplication rules for the double Schur functions and Cauchy identities. The Journal of Combinatorics, 16(1), R13-1-R13-44.
  • Molev, A. (2009). Littlewood-Richardson polynomials. Journal of Algebra, 321(11), 3450-3468. [More Information]
  • Chervov, A., Molev, A. (2009). On higher-order Sugawara operators. International Mathematics Research Notices, 2009 (9), 1612-1635. [More Information]
  • Futorny, V., Molev, A., Ovsienko, S. (2009). The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras. Advances in Mathematics, 223(3), 773-796. [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]
  • Futorny, V., Molev, A., Ovsienko, S. (2008). Gelfand-Tsetlin Bases for Representations of Finite W-Algebras and Shifted Yangians. VII International Workshop Lie theory and its applications in physics, Sofia, Bulgaria: Heron Publishing.
  • Molev, A. (2008). On the fusion procedure for the symmetric group. Reports on Mathematical Physics, 61(2), 181-188.
  • Isaev, A., Molev, A., Os'Kin, A. (2008). On the Idempotents of Hecke Algebras. Letters in Mathematical Physics, 85(1), 79-90. [More Information]
  • Molev, A., Ragoucy, E. (2008). Symmetries and invariants of twisted quantum algebras and associated Poisson algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 20(2), 173-198.

2007

  • Molev, A. (2007). Yangians and Classical Lie Algebras. Providence, RI, USA: American Mathematical Society.

2006

  • Hopkins, M., Molev, A. (2006). A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2, 092-1-092-29.
  • Molev, A. (2006). Gelfand-Tsetlin bases for classical Lie algebras. In M. Hazewinkel (Eds.), Handbook of algebra. Vol 4, (pp. 109-170). Amsterdam ; New York: Elsevier.
  • Arnaudon, D., Molev, A., Ragoucy, E. (2006). On the R-Matrix Realization of Yangians and their Representations. Annales Henri Poincare, 7, 1269-1325. [More Information]
  • Hopkins, M., Molev, A. (2006). On the skew representations of the quantum affine algebra. Czechoslovak Journal of Physics: europhysics journal, 56(10/11), 1179-1184. [More Information]
  • Molev, A. (2006). Representations of the twisted quantized enveloping algebra of type Cn. Moscow Mathematical Journal, 6(3), 531-551.
  • Molev, A. (2006). Skew representations of twisted Yangians. Selecta Mathematica - New Series, 12(1), 1-38. [More Information]
  • Billig, Y., Futorny, V., Molev, A. (2006). Verma modules for Yangians. Letters in Mathematical Physics, 78(1), 1-16. [More Information]

2005

  • Futorny, V., Molev, A., Ovsienko, S. (2005). Harish-Chandra modules for Yangians. Representation Theory, 9, 426-454.

2004

  • Bahturin, Y., Molev, A. (2004). Casimir elements for some graded Lie algebras and superalgebras. Czechoslovak Journal of Physics: europhysics journal, 54(11), 1159-1164. [More Information]
  • 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.
  • Molev, A., Retakh, V. (2004). Quasideterminants And Casimir Elements For The General Linear Lie Superalgebra. International Mathematics Research Notices, 2004 (13), 611-619.
  • Molev, A. (2004). The 8th Problem: Littlewood-Richardson problem for Schubert polynomials. Gazette of the Australian Mathematical Society, 31(5), 295-297.

2003

  • Molev, A. (2003). A new quantum analog of the Brauer algebra. Czechoslovak Journal of Physics: europhysics journal, 53(11), 1073-1078.
  • Molev, A., Ragoucy, E., Sorba, P. (2003). Coideal subalgebras in quantum affine algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 1(1), 789-822.
  • Molev, A. (2003). Yangians and their applications. In M. Hazelwinkel (Eds.), Handbook of Algebra. Vol 3, (pp. 909-959). Amsterdam ; London: Elsevier.

2002

  • Molev, A. (2002). Irreducibility criterion for tensor products of Yangian evaluation modules. Duke Mathematical Journal, 112(2), 307-341.
  • Molev, A., Ragoucy, E. (2002). Representations of reflection algebras. Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 14(3), 317-342.
  • Molev, A. (2002). Yangians and transvector algebras. Discrete Mathematics, 246(1), 231-253.

2001

  • Molev, A., Olshanski, G. (2001). Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Journal of Algebra, 237(1), 302-341.

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