Books

• A. Molev,
  Sugawara Operators for Classical Lie Algebras.
  Mathematical Surveys and Monographs, 229. American Mathematical Society, Providence, RI, 2018.
• Russian edition:
  Операторы Сугавары для классических алгебр Ли.
  МЦНМО, Москва, 2018.
• A. Molev,
  Yangians and Classical Lie Algebras.
  Mathematical Surveys and Monographs, 143. American Mathematical Society, Providence, RI, 2007. Errata
• Russian edition:
  Янгианы и классические алгебры Ли.
  МЦНМО, Москва, 2009.

Papers

• A. I. Molev,
  Representations of the super-Yangian of type D(n,m) ,
  preprint.
• A. Molev and E. Ragoucy,
  Representations of the super-Yangian of type B(n,m) ,
  preprint; J. Algebra, to appear.
• Y. Ikeda, A. Molev and G. Sharygin,
  On the quantum argument shift method ,
  preprint.
• N. Jing, M. Liu and A. Molev,
  Quantum Sugawara operators in type A ,
  preprint.
• N. Jing, M. Liu and A. Molev,
  Eigenvalues of quantum Gelfand invariants ,
  Journal of Mathematical Physics 65 (2024), 061703, 10 pp.
• A. Molev and E. Ragoucy,
  Gaussian generators for the Yangian associated with the Lie superalgebra osp(1|2m) ,
  Journal of Algebra 655 (2024), 722-757.
• A. I. Molev,
  A Drinfeld-type presentation of the orthosymplectic Yangians ,
  Algebras and Representation Theory 27 (2024), 469-494.
• A. I. Molev,
  Representations of the super Yangians of types A and C ,
  Algebras and Representation Theory 26 (2023), 1007-1027.
• A. I. Molev,
  Representations of the Yangians associated with Lie superalgebras osp(1|2n) ,
  Communications in Mathematical Physics 398 (2023), 541-571.
• A. I. Molev,
  Representations of the orthosymplectic Yangian ,
  preprint.
• A. I. Molev,
  W-algebras associated with centralizers in type A ,
  International Mathematics Research Notices 2022, 6019-6037.
• A. I. Molev,
  Odd reflections in the Yangian associated with gl(m|n) ,
  Letters in Mathematical Physics 112 (2022), no. 1, Paper No. 8, 15 pp.
• A. Molev and O. Yakimova,
  Monomial bases and branching rules ,
  Transformation Groups 26 (2021), 995-1024.
• A. I. Molev,
  On Segal-Sugawara vectors and Casimir elements for classical Lie algebras ,
  Letters in Mathematical Physics 111 (2021), no. 1, Paper No. 8, 23 pp.
• A. Molev, E. Ragoucy and U.R. Suh,
  Supersymmetric W-algebras ,
  Letters in Mathematical Physics 111 (2021), no. 1, Paper No. 6, 25 pp.
• A. I. Molev,
  Casimir elements and Sugawara operators for Takiff algebras ,
  Journal of Mathematical Physics 62 (2021), 011701, no. 1, 13 pp.
• A. I. Molev,
  Center at the critical level for centralizers in type A ,
  Journal of Algebra 566 (2021), 163-186.
• N. Jing, M. Liu and A. Molev,
  Representations of quantum affine algebras in their R-matrix realization ,
  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 16 (2020), 145, 25 pp.
• A. I. Molev and E. Ragoucy,
  Classical W-algebras for centralizers ,
  Communications in Mathematical Physics 378 (2020), 691-703.
• N. Jing, M. Liu and A. Molev,
  Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: types B and D ,
  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 16 (2020), 043, 49 pp.
• N. Jing, M. Liu and A. Molev,
  Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C ,
  Journal of Mathematical Physics 61 (2020), 031701, no. 3, 41 pp.
• A. Molev and O. Yakimova,
  Quantisation and nilpotent limits of Mishchenko-Fomenko subalgebras ,
  Representation Theory 23 (2019), 350-378.
• A. Molev and E. Ragoucy,
  Higher order Hamiltonians for the trigonometric Gaudin model ,
  Letters in Mathematical Physics 109 (2019), 2035-2048.
• N. Jing, M. Liu and A. Molev,
  Isomorphism between the R-matrix and Drinfeld presentations of Yangian in types B, C and D ,
  Communications in Mathematical Physics 361 (2018), 827-872.
• N. Jing, S. Kožić, A. Molev and F. Yang,
  Center of the quantum affine vertex algebra in type A ,
  Journal of Algebra 496 (2018), 138-186.
• A. I. Molev and E. E. Mukhin,
  Eigenvalues of Bethe vectors in the Gaudin model ,
  Theoretical and Mathematical Physics 192 (2017), 1258-1281.
• S. Kožić and A. Molev,
  Center of the quantum affine vertex algebra associated with trigonometric R-matrix ,
  Journal of Physics. A. Mathematical and Theoretical 50 (2017), 325201 (21pp).
• T. Arakawa and A. Molev,
  Explicit generators in rectangular affine W-algebras of type A ,
  Letters in Mathematical Physics 107 (2017), 47-59.
• A. I. Molev, E. Ragoucy and N. Rozhkovskaya,
  Segal-Sugawara vectors for the Lie algebra of type G_2 ,
  Journal of Algebra 455 (2016), 386-401.
• L. Frappat, N. Jing, A. Molev and E. Ragoucy,
  Higher Sugawara operators for the quantum affine algebras of type A ,
  Communications in Mathematical Physics 345 (2016), 631-657.
• V. Futorny and A. Molev,
  Quantization of the shift of argument subalgebras in type A ,
  Advances in Mathematics 285 (2015), 1358-1375.
• A. I. Molev and E. E. Mukhin,
  Invariants of the vacuum module associated with the Lie superalgebra gl(1|1) ,
  Journal of Physics. A. Mathematical and Theoretical 48 (2015), 314001 (20pp).
• A. I. Molev and E. Ragoucy,
  Classical W-algebras in types A, B, C, D and G ,
  Communications in Mathematical Physics 336 (2015), 1053-1084.
• T. Matsumoto and A. Molev,
  Representations of centrally extended Lie superalgebra psl(2|2) ,
  Journal of Mathematical Physics 55 (2014), Art. 091704.
• A. I. Molev and E. E. Mukhin,
  Yangian characters and classical W-algebras ,
  in "Conformal Field Theory, Automorphic Forms and Related Topics" (W. Kohnen, R. Weissauer, Eds), Springer, 2014, pp. 287-334.
• A. P. Isaev, A. I. Molev and O. V. Ogievetsky,
  Idempotents for Birman-Murakami-Wenzl algebras and reflection equation ,
  Advances in Theoretical and Mathematical Physics 18 (2014), 1-25.
• A. I. Molev and E. Ragoucy,
  The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for $\widehat{\mathfrak{gl}}_{m|n}$,
  Moscow Mathematical Journal 14 (2014), 83-119.
• A. I. Molev and N. Rozhkovskaya,
  Characteristic maps for the Brauer algebra ,
  Journal of Algebraic Combinatorics 38 (2013), 15-35.
• N. Iorgov, A. I. Molev and E. Ragoucy,
  Casimir elements from the Brauer-Schur-Weyl duality ,
  Journal of Algebra 387 (2013), 144-159.
• A. I. Molev,
  Feigin-Frenkel center in types B, C and D ,
  Inventiones mathematicae 191 (2013), 1-34.
• A. I. Molev,
  Pfaffian-type Sugawara operators ,
  preprint.
• A. P. Isaev, A. I. Molev and O. V. Ogievetsky,
  A new fusion procedure for the Brauer algebra and evaluation homomorphisms ,
  International Mathematics Research Notices (2012), 2571-2606.
• A. I. Molev,
  Combinatorial bases for covariant representations of the Lie superalgebra gl(m|n) ,
  Bulletin of the Institute of Mathematics, Academia Sinica 6 (2011), 415-462.
• Alexei Davydov and Alexander Molev,
  A categorical approach to classical and quantum Schur-Weyl duality,
  Contemporary Mathematics 537 (2011), 143-171.
• A. P. Isaev and A. I. Molev,
  Fusion procedure for the Brauer algebra,
  St. Petersburg Mathematical Journal 22 (2011), 437-446.
• Lucy Gow and Alexander Molev,
  Representations of twisted q-Yangians,
  Selecta Mathematica, New Series 16 (2010), 439-499.
• V. Futorny, A. Molev and S. Ovsienko,
  The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras,
  Advances in Mathematics 223 (2010), 773-796.
• A. I. Molev,
  Littlewood-Richardson polynomials,
  Journal of Algebra 321 (2009), 3450-3468.
• A. V. Chervov and A. I. Molev,
  On higher order Sugawara operators,
  International Mathematics Research Notices (2009), no. 9, 1612-1635.
• A. I. Molev,
  Comultiplication rules for the double Schur functions and Cauchy identities,
  Electronic Journal of Combinatorics 16(1) (2009), R13, 44pp.
• Y. Billig, A. Molev and R. Zhang,
  Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus,
  Advances in Mathematics 218 (2008), 1972-2004.
• A. P. Isaev, A. I. Molev and A. F. Os'kin,
  On the idempotents of Hecke algebras,
  Letters in Mathematical Physics 85 (2008), 79-90.
• A. I. Molev,
  On the fusion procedure for the symmetric group ,
  Reports on Mathematical Physics 61 (2008), 181-188.
• V. Futorny, A. Molev and S. Ovsienko,
  Gelfand-Tsetlin bases for representations of finite W-algebras and shifted Yangians,
  in "Lie theory and its applications in physics VII" (H.-D. Doebner and V.K. Dobrev, Eds)
  Proceedings of the VII International Workshop,
  Varna, Bulgaria, June 2007, Heron Press, Sofia, 2008, pp. 352-363.
• A. I. Molev and E. Ragoucy,
  Symmetries and invariants of twisted quantum algebras and associated Poisson algebras ,
  Reviews in Mathematical Physics 20 (2008), 173-198.
• M. J. Hopkins and A. I. Molev,
  A q-analogue of the centralizer construction and skew representations of the quantum affine algebra ,
  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2 (2006), paper 092, 29 pp.
• A. I. Molev,
  Representations of the twisted quantized enveloping algebra of type C_n ,
  Moscow Mathematical Journal, 6 (2006), 531--551.
• D. Arnaudon, A. Molev and E. Ragoucy,
  On the R-matrix realization of Yangians and their representations ,
  Annales Henri Poincaré, 7 (2006), 1269-1325.
• M. J. Hopkins and A. I. Molev,
  On the skew representations of the quantum affine algebra ,
  Czechoslovak Journal of Physics 56 (2006), 1179-1184.
• Y. Billig, V. Futorny and A. Molev,
  Verma modules for Yangians ,
  Letters in Mathematical Physics 78 (2006), 1-16.
• A. I. Molev,
  Skew representations of twisted Yangians ,
  Selecta Mathematica, New Series 12 (2006), 1-38.
• A. I. Molev,
  Gelfand-Tsetlin bases for classical Lie algebras ,
  in "Handbook of Algebra", Vol. 4, (M. Hazewinkel, Ed.), Elsevier, 2006, pp. 109-170.
• V. Futorny, A. Molev and S. Ovsienko,
  Harish-Chandra modules for Yangians ,
  Representation Theory, 9 (2005), 426 - 454.
• A. Molev,
  Littlewood-Richardson problem for Schubert polynomials ,
  Australian Mathematical Society Gazette, 31 (2004), 295 - 297.
• Yu. Bahturin and A. Molev,
  Casimir elements for some graded Lie algebras and superalgebras ,
  Czechoslovak Journal of Physics 54 (2004), 1159 - 1164.
• A. I. Molev, V. N. Tolstoy and R. B. Zhang,
  On irreducibility of tensor products of evaluation modules for the quantum affine algebra ,
  Journal of Physics. A. Mathematical and Theoretical 37 (2004), 2385 - 2399.
• A. Molev and V. Retakh,
  Quasideterminants and Casimir elements for the general linear Lie superalgebra,
  International Mathematics Research Notices, no. 13 (2004), 611-619.
• A. I. Molev, E. Ragoucy and P. Sorba,
  Coideal subalgebras in quantum affine algebras ,
  Reviews in Mathematical Physics 15 (2003), 789-822.
• A. I. Molev,
  Yangians and their applications ,
  in "Handbook of Algebra", Vol. 3, (M. Hazewinkel, Ed.), Elsevier, 2003, pp. 907-959.
• A. I. Molev,
  A new quantum analog of the Brauer algebra ,
  Czechoslovak Journal of Physics 53 (2003), 1073-1078.
• A. I. Molev and E. Ragoucy,
  Representations of reflection algebras ,
  Reviews in Mathematical Physics 14 (2002), 317-342.
• A. I. Molev,
  Irreducibility criterion for tensor products of Yangian evaluation modules ,
  Duke Mathematical Journal 112 (2002), 307-341.
• A. I. Molev,
  Yangians and transvector algebras,
  Discrete Mathematics 246 (2002), 231-253.
• A. I. Molev and G. I. Olshanski,
  Degenerate affine Hecke algebras and centralizer construction for the symmetric groups,
  Journal of Algebra 237 (2001), 302-341.
• A. I. Molev and G. I. Olshanski,
  Centralizer construction for twisted Yangians,
  Selecta Mathematica, New Series 6 (2000), 269-317.
• A. I. Molev,
  Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras,
  Journal of Physics. A. Mathematical and Theoretical 33 (2000), 4143-4168.
• A. I. Molev,
  A weight basis for representations of even orthogonal Lie algebras,
  in ``Combinatorial Methods in Representation Theory", Adv. Studies in Pure Math. 28 (2000), 221-240.
• A. I. Molev,
  On Gelfand-Tsetlin bases for representations of classical Lie algebras,
  in ``Proceedings of the 12-th International Conference FPSAC'00", Moscow, June 2000.
  Springer-Verlag 2000, pp. 300-308.
• A. I. Molev,
  A basis for representations of symplectic Lie algebras ,
  Communications in Mathematical Physics 201 (1999), 591-618.
• A. I. Molev and M. L. Nazarov,
  Capelli identities for classical Lie algebras ,
  Mathematische Annalen 313 (1999), 315-357.
• A. I. Molev and B. E. Sagan,
  A Littlewood-Richardson rule for factorial Schur functions ,
  Transactions of the American Mathematical Society 351 (1999), 4429-4443.
• A. I. Molev,
  A quantum Sylvester theorem and representations of Yangians ,
  in ``Proceedings of the 11-th Conference on Factorial Power Series and Algebraic Combinatorics",
  (C. Martinez, M. Noy and O. Serra, Eds), Barcelona, June 1999, pp. 379-387.
• A. I. Molev,
  On elementary representations of Yangians,
  in ``Group22: Proceedings of the XXII International Colloquium in Group Theoretical Methods in Physics",
  Hobart, 1998. Internat. Press, Cambridge, MA, 1999, pp. 433-437.
• A. I. Molev,
  Finite-dimensional irreducible representations of twisted Yangians ,
  Journal of Mathematical Physics 39 (1998), 5559-5600.
• A. I. Molev,
  Factorial supersymmetric Schur functions and super Capelli identities ,
  in ``Kirillov's Seminar on Representation Theory", (G. I. Olshanski, Ed.),
  Amer. Math. Soc. Transl., Ser. 2, Vol. 181, AMS, Providence, R.I., 1998, pp. 109-137.
• A. I. Molev,
  Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra ,
  Discrete Mathematics 180 (1998), 281-300.
• A. I. Molev and B. E. Sagan,
  A Pieri rule for generalized factorial Schur functions ,
  in ``Proceedings of the 9-th Conference on Factorial Power Series and Algebraic Combinatorics",
  Vienna, July 1997, Vol. 3, 517-523.
• A. I. Molev,
  Casimir elements for certain polynomial current Lie algebras [preprint version],
  in ``Group 21, Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras,"
  Vol. 1, (H.-D. Doebner, W. Scherer, P. Nattermann, Eds). World Scientific, Singapore, 1997, 172-176.
• A. Molev, M. Nazarov and G. Olshanskii,
  Yangians and classical Lie algebras ,
  Russian Mathematical Surveys 51 (1996), 205-282.
• A. Molev,
  A Remark on the Higher Capelli Identities,
  q-alg/9603007, [unpublished note].
• A. Molev,
  Noncommutative symmetric functions and Laplace operators for classical Lie algebras ,
  Letters in Mathematical Physics 35 (1995), 135-143.
• A. Molev,
  Sklyanin determinant, Laplace operators and characteristic identities for classical Lie algebras ,
  Journal of Mathematical Physics 36 (1995), 923-943.
• A. I. Molev,
  On Stirling partitions of the symmetric group ,
  ``Actes du 7eme Congres SFCA", (B. Leclerc, J.-Y. Thibon, Eds) Paris, May-June 1995, 435-447.
• A. I. Molev,
  Yangians and Laplace operators for classical Lie algebras,
  in ``Confronting the Infinite", Proceedings of the Conference in Celebration of the 70th Years of
  H. S. Green and C. A. Hurst. World Scientific, Singapore 1995, pp. 239-245.
• A. I. Molev,
  Gelfand-Tsetlin basis for representations of Yangians ,
  Letters in Mathematical Physics 30 (1994), 53-60.
• A. I. Molev,
  Russian translation of the book by V. Kac,
  Infinite-dimensional Lie algebras. Third edition. Cambridge University Press, Cambridge, 1990.
  Mir, Moscow, 1993.
• A. I. Molev,
  Representations of twisted Yangians ,
  Letters in Mathematical Physics 26 (1992), 211-218.
• A. I. Molev,
  On certain class of unitarizable representations of the Lie algebra u(p,q) ,
  in ``Proc. Winter School on Geometry and Physics", Srni, January 1990,
  Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, no. 26 (1991), 207-215.
• A. I. Molev,
  Unitarizability of some Enright-Varadarajan u(p,q)-modules ,
  in ``Topics in Representation Theory", (A. A. Kirillov Ed.),
  Advances in Soviet Mathematics, vol. 2, AMS, 1991, pp. 199-219.
• A. I. Molev,
  Gelfand-Tsetlin basis for irreducible unitarizable highest weight representations of u(p,q),
  Funkt. Anal. i Prilozh. 23 (1989), 76-77.
  English translation: Functional Analysis and Its Applications 23 (1989), 236-238.
• A. I. Molev,
  On the algebraic structure of the Lie algebra of vector fields on the line,
  Mat. Sb. (N.S.) 134(176) (1987), 82-92.
  English translation: Mathematics of the USSR-Sbornik 62 (1989), 83-94.
• A. I. Molev and L. M. Tsalenko,
  Representations of the symmetric group in a free Lie (super)algebra and in the space of harmonic polynomials,
  Funkt. Anal. i Prilozh. 20 (1986), 76-77.
  English translation: Functional Analysis and Its Applications 20 (1986), 150-152.
• A. I. Molev,
  On the growth of some Lie algebras of vector fields,
  Uspekhi Mat. Nauk 41 (1986), 205-206.
  English translation: Russian Mathematical Surveys 41 (1986), 213-214.
• A. A. Kirillov and A. I. Molev,
  Algebraic structure of a Lie algebra of vector fields,
  Keldysh Institute of Appl. Math. Preprint 168, Moscow, 1985.
  English translation: Selecta Mathematica Sovietica 9 (1990), 155-169.
• A. I. Molev,
  A proof of the Kirillov-Kontsevich formula,
  Uspekhi Mat. Nauk 39 (1984), 145-146.
  English translation: Russian Mathematical Surveys 39 (1984), 171-172.
• A. A. Kirillov, M. L. Kontsevich and A. I. Molev,
  Algebras of intermediate growth,
  Keldysh Institute of Appl. Math. Preprint 39, Moscow, 1983.
  English translation: Selecta Mathematica Sovietica 9 (1990), 137-153.