# Professor Alexander Molev

F07 - Carslaw Building
The University of Sydney

 Telephone 9351 5793 Fax 9351 4534 Email

## Research interests

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

AI_Molev

## Current research students

Project title Research student
Moduli spaces of geometric structures Alex CASELLA

## Awards and honours

2001: Medal of the Australian Mathematical Society

## Selected grants

### 2018

• Quantum vertex algebras; Molev A; Australian Research Council (ARC)/Discovery Projects (DP).

### 2015

• Classical and affine W-algebras; Molev A; Australian Research Council (ARC)/Discovery Projects (DP).

### 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

 Books Molev, A. (2007). Yangians and Classical Lie Algebras. Providence, RI, USA: American Mathematical Society. Book Chapters Molev, A., Mukhin, E. (2014). Yangian Characters and Classical W-Algebras. In Winfried Kohnen, Rainer Weissauer (Eds.), Conformal Field Theory, Automorphic Forms and Related Topics, (pp. 287-334). Berlin, Heidelberg: Springer Science+Business Media. [More Information] 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 Jing, N., Kozic, S., Molev, A., Yang, F. (2018). Center of the quantum affine vertex algebra in type $A$. Journal of Algebra, 496(Feb 2018), 138-186. [More Information] Kozic, S., Molev, A. (2017). Center of the quantum affine vertex algebra associated with trigonometric R-matrix. Journal of Physics A: Mathematical and General, 50(32), 1-21. [More Information] Molev, A., Mukhin, E. (2017). Eigenvalues of Bethe vectors in the Gaudin model. Theoretical and Mathematical Physics, 192(3), 1258-1281. [More Information] Arakawa, T., Molev, A. (2017). Explicit generators in rectangular affine $$\mathcal {W}$$ W-algebras of type A. Letters in Mathematical Physics, 107(1), 47-59. [More Information] Frappat, L., Naihuan, J., Molev, A., Ragoucy, E. (2016). Higher Sugawara Operators for the Quantum Affine Algebras of Type A. Communications in Mathematical Physics, 345, 631-657. [More Information] Molev, A., Ragoucy, E., Rozhkovskaya, N. (2016). Segal-Sugawara vectors for the Lie algebra of type G2. Journal of Algebra, 455, 386-401. [More Information] Molev, A., Ragoucy, E. (2015). Classical W-algebras in types A, B, C, D and G. Communications in Mathematical Physics, 336, 1053-1084. [More Information] Molev, A., Mukhin, E. (2015). Invariants of the vacuum module associated with the Lie superalgebra gl (1∣1). Journal of Physics A: Mathematical and Theoretical, 48(1), 1-20. [More Information] Futorny, V., Molev, A. (2015). Quantization of the shift of argument subalgebras in type A. Advances in Mathematics, 285, 1358-1375. [More Information] Isaev, A., Molev, A., Ogievetsky, O. (2014). Idempotents for Birman–Murakami–Wenzl algebras and reflection equation. Advances in Theoretical and Mathematical Physics, 18(1), 1-25. [More Information] Matsumoto, T., Molev, A. (2014). Representations of centrally extended Lie superalgebra psl(2|2). Journal of Mathematical Physics, 55(9), 1-22. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] Molev, A. (2002). Irreducibility criterion for tensor products of Yangian evaluation modules. Duke Mathematical Journal, 112(2), 307-341. [More Information] 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. [More Information] 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.
 2018 Jing, N., Kozic, S., Molev, A., Yang, F. (2018). Center of the quantum affine vertex algebra in type $A$. Journal of Algebra, 496(Feb 2018), 138-186. [More Information] 2017 Kozic, S., Molev, A. (2017). Center of the quantum affine vertex algebra associated with trigonometric R-matrix. Journal of Physics A: Mathematical and General, 50(32), 1-21. [More Information] Molev, A., Mukhin, E. (2017). Eigenvalues of Bethe vectors in the Gaudin model. Theoretical and Mathematical Physics, 192(3), 1258-1281. [More Information] Arakawa, T., Molev, A. (2017). Explicit generators in rectangular affine $$\mathcal {W}$$ W-algebras of type A. Letters in Mathematical Physics, 107(1), 47-59. [More Information] 2016 Frappat, L., Naihuan, J., Molev, A., Ragoucy, E. (2016). Higher Sugawara Operators for the Quantum Affine Algebras of Type A. Communications in Mathematical Physics, 345, 631-657. [More Information] Molev, A., Ragoucy, E., Rozhkovskaya, N. (2016). Segal-Sugawara vectors for the Lie algebra of type G2. Journal of Algebra, 455, 386-401. [More Information] 2015 Molev, A., Ragoucy, E. (2015). Classical W-algebras in types A, B, C, D and G. Communications in Mathematical Physics, 336, 1053-1084. [More Information] Molev, A., Mukhin, E. (2015). Invariants of the vacuum module associated with the Lie superalgebra gl (1∣1). Journal of Physics A: Mathematical and Theoretical, 48(1), 1-20. [More Information] Futorny, V., Molev, A. (2015). Quantization of the shift of argument subalgebras in type A. Advances in Mathematics, 285, 1358-1375. [More Information] 2014 Isaev, A., Molev, A., Ogievetsky, O. (2014). Idempotents for Birman–Murakami–Wenzl algebras and reflection equation. Advances in Theoretical and Mathematical Physics, 18(1), 1-25. [More Information] Matsumoto, T., Molev, A. (2014). Representations of centrally extended Lie superalgebra psl(2|2). Journal of Mathematical Physics, 55(9), 1-22. [More Information] 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. Molev, A., Mukhin, E. (2014). Yangian Characters and Classical W-Algebras. In Winfried Kohnen, Rainer Weissauer (Eds.), Conformal Field Theory, Automorphic Forms and Related Topics, (pp. 287-334). Berlin, Heidelberg: Springer Science+Business Media. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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. [More Information] 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.