@article{TMF_2023_216_2_a2,
author = {A. Yu. Orlov},
title = {Polygon gluing and commuting bosonic operators},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {234--244},
year = {2023},
volume = {216},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a2/}
}
A. Yu. Orlov. Polygon gluing and commuting bosonic operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a2/
[1] A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Polnyi nabor operatorov razrezaniya i skleiki v teorii Gurvitsa–Kontsevicha”, TMF, 166:1 (2011), 3–27, arXiv: 0904.4227 | DOI | DOI | MR
[2] A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, Universal algebras of Hurwitz numbers, arXiv: 0909.1164
[3] A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Algebra of differential operators associated with Young diagramms”, J. Geom. Phys., 62:2 (2012), 148–155, arXiv: 1012.0433 | DOI | MR
[4] A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations”, JHEP, 11 (2011), 097, 32 pp., arXiv: 1108.0885 | DOI | MR
[5] A. I. Molev, M. L. Nazarov, G. I. Olshanskii, “Yangiany i klassicheskie algebry Li”, UMN, 51:2(308) (1996), 27–104, arXiv: hep-th/9409025 | DOI | DOI | MR | Zbl
[6] A. B. Zheglov, “Algebraic geometric properties of spectral surfaces of quantum integrable systems and their isospectral deformations”, in Geometric Methods in Physics XXXVIII (Workshop, Białowei.{z}a, Poland, 2019), Trends in Mathematics, eds. P. Kielanowski, A. Odzijewicz, E. Previato, Birkhäuser, Cham, 2020, 313–331 ; А. Б. Жеглов, “Теория Шура–Сато для квазиэллиптических колец”, Алгебра, арифметическая, алгебраическая и комплексная геометрия, Сборник статей. Посвящается памяти академика Алексея Николаевича Паршина, Труды МИАН, 320, МИАН, М., 2023, 128–176 | DOI | MR | DOI | DOI | MR
[7] S. M. Natanzon, A. Yu. Orlov, “Hurwitz numbers from matrix integrals over Gaussian measure”, Integrability, Quantization, and Geometry, Proceedings of Symposia in Pure Mathematics, 103.1, eds. S. Novikov, I. Krichever, O. Ogievetsky, S. Shlosman, AMS, Providence, RI, 2021, 337–375, arXiv: 2002.00466 | DOI | MR
[8] S. M. Natanzon, A. Yu. Orlov, “Chisla Gurvitsa, poluchayuschiesya iz feinmanovskikh diagramm”, TMF, 204:3 (2020), 396–429, arXiv: 2006.07396 | DOI | DOI
[9] D. Gurevich, P. Saponov, D. Talalaev, “KZ equations and Bethe subalgebras in generalized Yangians related to compatible $R$-matrices”, J. Integrable Syst., 4:1 (2019), xyz005, 18 pp. | DOI | MR
[10] N. A. Slavnov, “Algebraicheskii anzats Bete i kvantovye integriruemye sistemy”, UMN, 62:4(376) (2007), 91–132 | DOI | DOI | MR | Zbl
[11] G. I. Olshanskii, “Yangiany i universalnye obertyvayuschie algebry”, Differentsialnaya geometriya, gruppy Li i mekhanika. IX, Zap. nauch. sem. LOMI, 164, Izd-vo “Nauka”, Leningrad. otd., L., 1987, 142–150 | DOI | Zbl
[12] G. I. Olshanski, “Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians”, Topics in Representation Theory, Advances in Soviet Mathematics, 2, ed. A. A. Kirillov, AMS, Providence, RI, 1991, 1–66 | MR | Zbl
[13] A. Okounkov, “Quantum immanants and higher Capelli identities”, Transform. Groups, 1:1–2 (1996), 99–126 | DOI | MR | Zbl
[14] A. Okounkov, “Young basis, Wick formula, and higher Capelli identities”, Internat. Math. Res. Notices, 1996, no. 17, 817–839 | DOI | MR
[15] M. Nazarov, G. Olshanski, “Bethe subalgebras in twisted Yangians”, Commun. Math. Phys., 178:2 (1996), 483–506 | DOI | MR
[16] M. Nazarov, E. Sklyanin, “Integrable hierarchy of the quantum Benjamin–Ono equation”, SIGMA, 9 (2013), 078, 14 pp., arXiv: 1309.6464 | DOI | MR
[17] G. I. Sharygin, “$L_\infty$-derivations and the argument shift method for deformation quantization algebras”, Acta Math. Sci., 1 (2021), 61–86, arXiv: 1912.00586 | DOI
[18] G. Sharygin, “Deformation quantization and the action of Poisson vector fields”, Lobachevskii J. Math., 38:6 (2017), 1093–1107, arXiv: 1612.02673 | DOI | MR
[19] D. Gurevich, P. Pyatov, P. Saponov, “Braided Weyl algebras and differential calculus on $U(u(2))$”, J. Geom. Phys., 62:5 (2012), 1175–1188, arXiv: 1112.6258 | DOI | MR
[20] N. Reshetikhin, Spin Calogero–Moser periodic chains and two dimensional Yang–Mills theory with corners, arXiv: 2303.10579
[21] A. N. Sergeev, A. P. Veselov, “Dunkl operators at infinity and Calogero–Moser systems”, Int. Math. Res. Notices, 2015:21 (2015), 10959–10986 | DOI | MR
[22] D. Gurevich, V. Petrova, P. Saponov, $q$-Casimir and $q$-cut-and-join operators related to reflection equation algebras, arXiv: 2110.04354
[23] I. Makdonald, Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1984 | MR
[24] Ya. Ikeda, “Kvazidifferentsialnyi operator i kvantovyi metod sdviga invariantov”, TMF, 212:1 (2022), 33–39 | DOI | DOI | MR
[25] Ya. Amborn, L. O. Chekhov, “Matrichnaya model dlya gipergeometricheskikh chisel Gurvitsa”, TMF, 181:3 (2014), 421–435, arXiv: 1409.3553 | DOI | DOI | MR
[26] A. M. Perelomov, V. S. Popov, “Operatory Kazimira dlya klassicheskikh grupp”, Dokl. AN SSSR, 174:2 (1967), 287–290 | MR | Zbl
[27] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, MTsNMO, M., 2007 | DOI | MR | Zbl
[28] A. K. Zvonkin, S. K. Lando, Grafy na poverkhnostyakh i ikh prilozheniya, MTsNMO, M., 2010 | MR