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УМН, 1996, том 51, выпуск 2(308), страницы 27–104 (Mi umn944)  

Эта публикация цитируется в 153 научных статьях (всего в 154 статьях)

Янгианы и классические алгебры Ли

А. И. Молевa, М. Л. Назаровb, Г. И. Ольшанскийc

a University of Sydney
b University of New South Wales
c Институт проблем передачи информации РАН

DOI: https://doi.org/10.4213/rm944

Полный текст: PDF файл (596 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Russian Mathematical Surveys, 1996, 51:2, 205–282

Реферативные базы данных:

УДК: 512.5
MSC: 17B37, 17B35
Поступила в редакцию: 23.03.1995

Образец цитирования: А. И. Молев, М. Л. Назаров, Г. И. Ольшанский, “Янгианы и классические алгебры Ли”, УМН, 51:2(308) (1996), 27–104; Russian Math. Surveys, 51:2 (1996), 205–282

Цитирование в формате AMSBIB
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    Эта публикация цитируется в следующих статьяx:
    1. A. I. Molev, “Finite-dimensional irreducible representations of twisted Yangians”, J Math Phys (N Y ), 39:10 (1998), 5559  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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    5. Khoroshkin, SM, “Deformation of Yangian Y(sl(2))”, Communications in Algebra, 26:4 (1998), 1041  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    7. Nazarov, M, “On irreducibility of tensor products of Yangian modules”, International Mathematics Research Notices, 1998, no. 3, 125  crossref  mathscinet  isi  elib
    8. Molev, AI, “Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra”, Discrete Mathematics, 180:1–3 (1998), 281  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. M Mintchev, E Ragoucy, P Sorba, Ph Zaugg, J Phys A Math Gen, 32:32 (1999), 5885  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Nazarov, M, “Yangian of the queer Lie superalgebra”, Communications in Mathematical Physics, 208:1 (1999), 195  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    11. Arakawa, T, “Drinfeld functor and finite-dimensional representations of Yangian”, Communications in Mathematical Physics, 205:1 (1999), 1  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. Molev, AI, “A basis for representations of symplectic Lie algebras”, Communications in Mathematical Physics, 201:3 (1999), 591  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    13. Molev, A, “Capelli identities for classical Lie algebras”, Mathematische Annalen, 313:2 (1999), 315  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    15. Tôru Umeda, Takeshi Hirai, “On Turnbull identity for skew-symmetric matrices”, Proc Edin Math Soc, 43:2 (2000), 379  crossref  mathscinet  zmath  isi  scopus  scopus
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    18. Molev A.I., “A weight basis for representations of even orthogonal Lie algebras”, Combinatorial Methods in Representation Theory, Advanced Studies in Pure Mathematics, 28, 2000, 221–240  mathscinet  zmath  isi
    19. Molev A.I., “On Gelfand-Tsetlin bases for representations of classical Lie algebras”, Formal Power Series and Algebraic Combinatorics, 2000, 300–308  crossref  mathscinet  zmath  isi
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    29. N J MacKay, “Rational K-matrices and representations of twisted Yangians”, J Phys A Math Gen, 35:37 (2002), 7865  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    30. Tarasov, V, “Duality for Knizhnik–Zamolodchikov and dynamical equations”, Acta Applicandae Mathematicae, 73:1–2 (2002), 141  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    31. Molev, AI, “Irreducibility criterion for tensor products of Yangian evaluation modules”, Duke Mathematical Journal, 112:2 (2002), 307  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    32. Nazarov, M, “On irreducibility of tensor products of Yangian modules associated with skew Young diagrams”, Duke Mathematical Journal, 112:2 (2002), 343  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    34. Molev, AI, “Yangians and transvector algebras”, Discrete Mathematics, 246:1–3 (2002), 231  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    35. C Briot, E Ragoucy, “ -superalgebras as truncations of super-Yangians”, J Phys A Math Gen, 36:4 (2003), 1057  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    36. P D Jarvis, G Rudolph, “Polynomial super-gl(n) algebras”, J Phys A Math Gen, 36:20 (2003), 5531  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    37. D. Arnaudon, J. Avan, N. Crampé, L. Frappat, E. Ragoucy, “R-matrix presentation for super-Yangians Y(osp(m∣2n))”, J Math Phys (N Y ), 44:1 (2003), 302  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    38. C. Briot, E. Ragoucy, “Twisted super-Yangians and their representations”, J Math Phys (N Y ), 44:3 (2003), 1252  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    39. Molev, AI, “Coideal subalgebras in quantum affine algebras”, Reviews in Mathematical Physics, 15:8 (2003), 789  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    40. Umeda, T, “Application of Koszul complex to Wronski relations for U(g(l)n)”, Commentarii Mathematici Helvetici, 78:4 (2003), 663  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    41. Arnaudon, D, “Classification of reflection matrices related to (super-)Yangians and application to open spin chain models”, Nuclear Physics B, 668:3 (2003), 469  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    42. MacKay, NJ, “Boundary scattering, symmetric spaces and the principal chiral model on the half-line”, Communications in Mathematical Physics, 233:2 (2003), 313  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    43. Delius, GW, “Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line”, Communications in Mathematical Physics, 233:1 (2003), 173  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    44. D Arnaudon, J Avan, N Crampé, A Doikou, L Frappat, E Ragoucy, “General boundary conditions for the $sl(\scr N)$ and $sl(\scr M\vert \scr N)$ open spin chains”, J Stat Mech Theor Exp, 2004:8 (2004), P08005  crossref  mathscinet  zmath  isi  scopus  scopus
    45. A I Molev, V N Tolstoy, R B Zhang, “On irreducibility of tensor products of evaluation modules for the quantum affine algebra”, J Phys A Math Gen, 37:6 (2004), 2385  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    46. V Caudrelier, N Crampé, “Integrable N-particle Hamiltonians with Yangian or reflection algebra symmetry”, J Phys A Math Gen, 37:24 (2004), 6285  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    47. Nazarov, M, “Rational representations of Yangians associated with skew Young diagrams”, Mathematische Zeitschrift, 247:1 (2004), 21  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    48. Molev, A, “Quasideterminants and Casimir elements for the general linear Lie superalgebra”, International Mathematics Research Notices, 2004, no. 13, 611  crossref  mathscinet  zmath  adsnasa  isi  elib
    49. Gerasimov, A, “Representation theory and quantum inverse scattering method: The open Toda chain and the hyperbolic Sutherland model”, International Mathematics Research Notices, 2004, no. 17, 823  crossref  mathscinet  zmath  isi  elib
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    51. Lucy Gow, “On the Yangian Y $(\mathfrak{g}\mathfrak{l}_{m|n} )$ and its quantum Berezinian”, Czech J Phys, 55:11 (2005), 1415  crossref  mathscinet  isi  scopus  scopus
    52. D Arnaudon, N Crampé, A Doikou, L Frappat, É Ragoucy, “Analytical Bethe ansatz for closed and open $gl(N)$-spin chains in any representation”, J Stat Mech Theor Exp, 2005:2 (2005), P02007  crossref  mathscinet  isi  scopus  scopus
    53. Anastasia Doikou, “On reflection algebras and twisted Yangians”, J Math Phys (N Y ), 46:5 (2005), 053504  crossref  mathscinet  zmath  isi  scopus  scopus
    54. Mackay, NJ, “Introduction to Yangian symmetry in integrable field theory”, International Journal of Modern Physics A, 20:30 (2005), 7189  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    55. Futorny, V, “Kostant's theorem for special filtered algebras”, Bulletin of the London Mathematical Society, 37 (2005), 187  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    57. Brundan, J, “Parabolic presentations of the Yangian Y (gl(n))”, Communications in Mathematical Physics, 254:1 (2005), 191  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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    59. Tarasov V., “Duality for Knizhinik-Zamolodchikov and dynamical equations, and hypergeometric integrals”, Infinite Dimensional Algebras and Quantum Integrable Systems, Progress in Mathematics, 237, 2005, 235–263  crossref  mathscinet  zmath  isi  scopus  scopus
    60. Н. Д. МакКай, “Интегрируемость нелинейных сигма-моделей с границей”, ТМФ, 142:2 (2005), 322–328  mathnet  crossref  mathscinet  zmath  adsnasa  elib; N. J. MacKay, “Boundary integrability of nonlinear sigma models”, Theoret. and Math. Phys., 142:2 (2005), 270–274  crossref  isi
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    63. E Mukhin, V Tarasov, A Varchenko, “Bethe eigenvectors of higher transfer matrices”, J Stat Mech Theor Exp, 2006:8 (2006), P08002  crossref  mathscinet  isi  scopus  scopus
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