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2025 |
1. |
A. V. Zotov, “On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion”, Funkts. analiz i ego pril., 59:2 (2025) (to appear) ; (to appear) |
2. |
R. A. Potapov, A. V. Zotov, “Interrelations between dualities in classical integrable systems and a classical–classical version of the quantum–classical duality”, Theoret. and Math. Phys., 222:2 (2025), 252–275 |
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2024 |
3. |
M. Matushko, A. Zotov, “Supersymmetric generalization of $q$-deformed long-range spin chains of Haldane–Shastry type and trigonometric $\mathrm{GL}(N|M)$ solution of associative Yang–Baxter equation”, Nuclear Phys. B, 1001 (2024), 116499 , 14 pp., arXiv: 2312.04525 ; |
4. |
K. R. Atalikov, A. V. Zotov, “Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model”, Theoret. and Math. Phys., 219:3 (2024), 1004–1017 |
5. |
Andrei Zotov, “Non-ultralocal classical $r$-matrix structure for $1+1$ field analogue of elliptic Calogero–Moser model”, J. Phys. A, 57 (2024), 315201 , 28 pp., arXiv: 2404.01898 ; |
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2023 |
6. |
M. Matushko, A. Zotov, “Elliptic generalisation of integrable $q$-deformed anisotropic Haldane–Shastry long-range spin chain”, Nonlinearity, 36:1 (2023), 319 , 36 pp., arXiv: 2202.01177 ; |
7. |
JETP Letters, 117:8 (2023), 630–634 |
8. |
K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, Theoret. and Math. Phys., 216:2 (2023), 1083–1103 , arXiv: 2303.02391 |
9. |
M. Matushko, Andrei Zotov, “Anisotropic spin generalization of elliptic Macdonald–Ruijsenaars operators and $R$-matrix identities”, Ann. Henri Poincaré, 24 (2023), 3373–3419 , arXiv: 2201.05944 ; |
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2022 |
10. |
A. Gorsky, M. Vasilyev, A. Zotov, “Dualities in quantum integrable many-body systems and integrable probabilities. Part I”, JHEP, 2022:4 (2022), 159 , 86 pp., arXiv: 2109.05562 ; |
11. |
A. Levin, M. Olshanetsky, A. Zotov, “2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles”, Eur. Phys. J. C, Part. Fields, 82 (2022), 635 , 14 pp., arXiv: 2202.10106 ; |
12. |
A. Zabrodin, A. Zotov, “Field analogue of the Ruijsenaars–Schneider model”, JHEP, 2022:7 (2022), 23 , 51 pp., arXiv: 2107.01697 ; |
13. |
K. Atalikov, A. Zotov, “Higher Rank 1 + 1 Integrable Landau–Lifshitz Field Theories from the Associative Yang–Baxter Equation”, JETP Letters, 115 (2022), 757-762 , arXiv: 2204.12576 |
14. |
E. Trunina, A. Zotov, “Lax equations for relativistic $\mathrm{G}\mathrm{L}(NM,\mathbb{C})$ Gaudin models on elliptic curve”, J. Phys. A, 55:39 (2022), 395202 , 31 pp., arXiv: 2204.06137 ; |
15. |
M. G. Matushko, A. V. Zotov, “On the $R$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators”, Theoret. and Math. Phys., 213:2 (2022), 1543–1559 , arXiv: 2211.08529 |
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2021 |
16. |
K. Atalikov, A. Zotov, “Field theory generalizations of two-body Calogero–Moser models in the form of Landau–Lifshitz equations”, J. Geom. Phys., 164 (2021), 104161 , 14 pp., arXiv: 2010.14297 ; |
17. |
A. Grekov, A. Zotov, “Characteristic determinant and Manakov triple for the double elliptic integrable system”, SciPost Phys., 10:3 (2021), 055 , 34 pp., arXiv: 2010.08077 ; |
18. |
I. A. Sechin, A. V. Zotov, Theoret. and Math. Phys., 208:2 (2021), 1156–1164 , arXiv: 2104.04963 |
19. |
E. S. Trunina, A. V. Zotov, “Multi-pole extension of the elliptic models of interacting integrable tops”, Theoret. and Math. Phys., 209:1 (2021), 1331–1356 , arXiv: 2104.08982 |
20. |
A. Levin, M. Olshanetsky, A. Zotov, “Generalizations of parabolic Higgs bundles, real structures, and integrability”, J. Math. Phys., 62:10 (2021), 103502 , 28 pp., arXiv: 2012.15529 ; |
21. |
A. Grekov, A. Zotov, “On Cherednik and Nazarov–Sklyanin large $N$ limit construction for integrable many-body systems with elliptic dependence on momenta”, JHEP, 2021:12 (2021), 062 , 43 pp., arXiv: 2102.06853 ; |
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2020 |
22. |
Sovremennye problemy matematicheskoi i teoreticheskoi fiziki, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Andreya Alekseevicha Slavnova, Trudy MIAN, 309, ed. A. K. Pogrebkov, N. A. Slavnov, A. A. Belavin, A. V. Zotov, I. V. Tyutin, MIAN, M., 2020 , 346 pp. |
23. |
M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical duality for Gaudin magnets with boundary”, Nuclear Phys. B, 952 (2020), 114931 , 20 pp., arXiv: 1911.11792 ; |
24. |
A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetrization of elliptic $R$-matrices”, J. Phys. A, 53:18 (2020), 185202 , 16 pp., arXiv: 1910.05712 ; |
25. |
N. Slavnov, A. Zabrodin, A. Zotov, “Scalar products of Bethe vectors in the 8-vertex model”, JHEP, 2020:6 (2020), 123 , 53 pp., arXiv: 2005.11224 ; |
26. |
I. A. Sechin, A. V. Zotov, “Integrable system of generalized relativistic interacting tops”, Theoret. and Math. Phys., 205:1 (2020), 1292–1303 , arXiv: 2011.09599 |
27. |
A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations”, J. Math. Phys., 61 (2020), 103504 , 9 pp., arXiv: 1910.01814 ; |
28. |
M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary”, J. Phys. A, 53:49 (2020), 494002 , 20 pp., arXiv: 2006.06717 ; |
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2019 |
29. |
A. Grekov, A. Zabrodin, A. Zotov, “Supersymmetric extension of qKZ-Ruijsenaars correspondence”, Nuclear Phys. B, 939 (2019), 174–190 , arXiv: 1810.12658 |
30. |
Yu. Chernyakov, S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Generalized Calogero and Toda models”, JETP Letters, 109:2 (2019), 136–143 |
31. |
I. A. Sechin, A. V. Zotov, “${\rm GL}_{NM}$ quantum dynamical $R$-matrix based on solution of the associative Yang–Baxter equation”, Russian Math. Surveys, 74:4 (2019), 767–769 , arXiv: 1905.08724 |
32. |
T. Krasnov, A. Zotov, “Trigonometric Integrable Tops from Solutions of Associative Yang–Baxter Equation”, Ann. Henri Poincaré, 20:8 (2019), 2671–2697 , arXiv: 1812.04209 |
33. |
A. V. Zotov, “Relativistic interacting integrable elliptic tops”, Theoret. and Math. Phys., 201:2 (2019), 1563–1578 , arXiv: 1910.08246 |
34. |
A. Grekov, I. Sechin, A. Zotov, “Generalized model of interacting integrable tops”, JHEP, 2019:10 (2019), 81 , 33 pp., arXiv: 1905.07820 |
35. |
M. Vasilyev, A. Zotov, “On factorized Lax pairs for classical many-body integrable systems”, Rev. Math. Phys., 31:6 (2019), 1930002 , 45 pp., arXiv: 1804.02777 |
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2018 |
36. |
I. Sechin, A. Zotov, “R-matrix-valued Lax pairs and long-range spin chains”, Phys. Lett. B, 781 (2018), 1–7 , arXiv: 1801.08908 |
37. |
A. Grekov, A. Zotov, “On $R$-matrix valued Lax pairs for Calogero–Moser models”, J. Phys. A, 51 (2018), 315202 , 26 pp., arXiv: 1801.00245 |
38. |
A. V. Zabrodin, A. V. Zotov, “Self–dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian”, Nuclear Phys. B, 927 (2018), 550–565 , arXiv: 1711.01036 |
39. |
A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770 |
40. |
S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Quasi-compact Higgs bundles and Calogero–Sutherland systems with two types of spins”, J. Math. Phys., 59:10 (2018), 103509 , 36 pp., arXiv: 1712.08851 |
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2017 |
41. |
A. Zabrodin, A. Zotov, “KZ-Calogero correspondence revisited”, J. Phys. A, 50 (2017), 205202 , 12 pp., arXiv: 1701.06074 |
42. |
A. V. Zabrodin, A. V. Zotov, A. N. Liashyk, D. S. Rudneva, “Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles”, Theoret. and Math. Phys., 192:2 (2017), 1141–1153 , arXiv: 1611.02497 |
43. |
A. Zabrodin, A. Zotov, “QKZ–Ruijsenaars correspondence revisited”, Nuclear Phys. B, 922 (2017), 113–125 , arXiv: 1704.04527 |
44. |
JETP Letters, 106:3 (2017), 179–183 |
45. |
A. Zotov, “Relativistic elliptic matrix tops and finite Fourier transformations”, Modern Phys. Lett. A, 32:32 (2017), 1750169 , 22 pp., arXiv: 1706.05601 |
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2016 |
46. |
A. Levin, M. Olshanetsky, A. Zotov, “Yang–Baxter equations with two Planck constants”, J. Phys. A: Math. Theor., 49:1 (2016), 14003 , 19 pp., Exactly Solved Models and Beyond: a special issue in honour of R. J. Baxter's 75th birthday, arXiv: 1507.02617 |
47. |
M. Beketov, A. Liashyk, A. Zabrodin, A. Zotov, “Trigonometric version of quantum–classical duality in integrable systems”, Nuclear Phys. B, 903 (2016), 150–163 , arXiv: 1510.07509 |
48. |
Ivan Sechin, Andrei Zotov, “Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices”, J. Math. Phys., 57:5 (2016), 53505 , 14 pp., arXiv: 1511.08761 |
49. |
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations”, Theoret. and Math. Phys., 188:2 (2016), 1121–1154 , arXiv: 1507.04265 |
50. |
Andrey Levin, Mikhail Olshanetsky, Andrei Zotov, “Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation”, J. Phys. A, 49:39 (2016), 395202 , 26 pp., arXiv: 1603.06101 |
51. |
A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, Theoret. and Math. Phys., 189:2 (2016), 1554–1562 |
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2015 |
52. |
G. Aminov, H. W. Braden, A. Mironov, A. Morozov, A. Zotov, “Seiberg-Witten curves and double-elliptic integrable systems”, J. High Energy Phys., 2015, no. 1, 033 , 15 pp., arXiv: 1410.0698 |
53. |
G. Aminov, A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and Knizhnik–Zamolodchikov–Bernard equations”, JETP Letters, 101:9 (2015), 648–655 |
54. |
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423 , arXiv: 1212.5813 |
55. |
Zengo Tsuboi, Anton Zabrodin, Andrei Zotov, “Supersymmetric quantum spin chains and classical integrable systems”, J. High Energy Phys., 2015, no. 5, 086 , 43 pp., arXiv: 1412.2586 |
56. |
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Quantum Baxter–Belavin $R$-matrices and multidimensional Lax pairs for Painlevé VI”, Theoret. and Math. Phys., 184:1 (2015), 924–939 , arXiv: 1501.07351 |
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2014 |
57. |
A. Gorsky, A. Zabrodin, A. Zotov, “Spectrum of quantum transfer matrices via classical many-body systems”, J. High Energy Phys., 2014, no. 1, 070 , 28 pp., arXiv: 1310.6958 |
58. |
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118 , arXiv: 1311.4498 |
59. |
G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, “Rational top and its classical $r$-matrix”, J. Phys. A: Math. Theor., 47:30 (2014), 305207 , 19 pp., arXiv: 1402.3189 |
60. |
A. Levin, M. Olshanetsky, A. Zotov, “Relativistic classical integrable tops and quantum $R$-matrices”, J. High Energy Phys., 2014, no. 7, 012 , arXiv: 1405.7523 |
61. |
A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and soliton equations related to eleven-vertex $R$-matrix”, Nuclear Physics B, 887 (2014), 400–422 , arXiv: 1406.2995 |
62. |
A. Levin, M. Olshanetsky, A. Zotov, “Planck constant as spectral parameter in integrable systems and KZB equations”, JHEP, 2014, no. 10, 109 , 29 pp., arXiv: 1408.6246v2 |
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2013 |
63. |
JETP Letters, 97:1 (2013), 45–51 |
64. |
A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral duality between Heisenberg chain and Gaudin model”, Lett. Math. Phys., 103:3 (2013), 299–329 , arXiv: 1206.6349 |
65. |
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes of $\mathrm{SL}(N,\mathbb C)$-bundles and quantum dynamical elliptic $R$-matrices”, J. Phys. A: Math. Theor., 46:3 (2013), 035201 , 25 pp., arXiv: 1208.5750 |
66. |
A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338 |
67. |
G. Aminov, A. Mironov, A. Morozov, A. Zotov, “Three-particle integrable systems with elliptic dependence on momenta and theta function identities”, Phys. Lett. B, 726:4-5 (2013), 802–808 , arXiv: 1307.1465 |
68. |
A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral dualities in XXZ spin chains and five dimensional gauge theories”, J. High Energy Phys., 2013, no. 12, 034 , 11 pp., arXiv: 1307.1502 |
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2012 |
69. |
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes and Hitchin systems. General construction”, Comm. Math. Phys., 316:1 (2012), 1–44 , arXiv: 1006.0702 |
70. |
A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence for Painlevé VI”, J. Math. Phys., 53:7 (2012), 073508 , 19 pp., arXiv: 1107.5672 |
71. |
A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence”, J. Math. Phys., 53:7 (2012), 073507 , 19 pp., arXiv: 1107.5672 |
72. |
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Calogero-Moser systems for simple Lie groups and characteristic classes of bundles”, J. Geom. Phys., 62:8 (2012), 1810–1850 , arXiv: 1007.4127 |
73. |
Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095 , 37 pp., arXiv: 1207.4386 |
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2011 |
74. |
Andrei V. Zotov, “1+1 Gaudin Model”, SIGMA, 7 (2011), 067 , 26 pp., arXiv: 1012.1072 |
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2009 |
75. |
Andrey M. Levin, Mikhail A. Olshanetsky, Andrei V. Zotov, “Monopoles and Modifications of Bundles over Elliptic Curves”, SIGMA, 5 (2009), 065 , 22 pp., arXiv: 0811.3056 |
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2008 |
76. |
A. V. Zotov, A. M. Levin, M. A. Olshanetsky, Yu. B. Chernyakov, “Quadratic algebras related to elliptic curves”, Theoret. and Math. Phys., 156:2 (2008), 1103–1122 , arXiv: 0710.1072 |
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