Polygon gluing and commuting bosonic operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 234-244 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two families of commuting Hamiltonians are constructed, parameterized by a constant matrix. The first series is new and the second is known, and in our approach follows from the first series. For the proof, we use known facts on the relations between random matrices and Hurwitz numbers, but the text is selfcontained and does not require acquaintance with previous work.
Keywords: polygon gluing, commuting quantum Hamilonians.
@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/}
}
TY  - JOUR
AU  - A. Yu. Orlov
TI  - Polygon gluing and commuting bosonic operators
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 234
EP  - 244
VL  - 216
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a2/
LA  - ru
ID  - TMF_2023_216_2_a2
ER  - 
%0 Journal Article
%A A. Yu. Orlov
%T Polygon gluing and commuting bosonic operators
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 234-244
%V 216
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a2/
%G ru
%F 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