Geodesic
Second-order quantum argument shifts in $Ugl_d$
Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 2, pp. 275-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe an explicit formula for the second-order quantum argument shifts of an arbitrary central element of the universal enveloping algebra of a general linear Lie algebra. We identify the generators of the subalgebra generated by the quantum argument shifts up to the second order.
Keywords: universal enveloping algebra, Lie algebra, quantum argument shift method
Mots-clés : deformation quantization. 
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Y. Ikeda. Second-order quantum argument shifts in $Ugl_d$. Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 2, pp. 275-285. http://geodesic.mathdoc.fr/item/TMF_2024_220_2_a3/

[1] A. S. Mischenko, A. T. Fomenko, “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 396–415 | DOI | MR | Zbl

[2] E. B. Vinberg, “O nekotorykh kommutativnykh podalgebrakh universalnoi obertyvayuschei algebry”, Izv. AN SSSR. Ser. matem., 54:1 (1990), 3–25 | DOI | MR | Zbl

[3] M. Nazarov, G. Olshanski, “Bethe subalgebras in twisted Yangians”, Commun. Math. Phys., 178:2 (1996), 483–506 | DOI | MR

[4] A. A. Tarasov, “O nekotorykh kommutativnykh podalgebrakh v universalnoi obertyvayuschei algebre algebry Li $\mathfrak{gl}(n,\mathbb C)$”, Matem. sb., 191:9 (2000), 115–122 | DOI | DOI | MR | Zbl

[5] L. G. Rybnikov, “Metod sdviga invariantov i model Godena”, Funkts. analiz i ego pril., 40:3 (2006), 30–43 | DOI | DOI | MR | Zbl

[6] B. Feigin, E. Frenkel, V. Toledano Laredo, “Gaudin models with irregular singularities”, Adv. Math., 223:3 (2010), 873–948 | DOI | MR

[7] V. Futorny, A. Molev, “Quantization of the shift of argument subalgebras in type $A$”, Adv. Math., 285 (2015), 1358–1375 | DOI | MR

[8] A. Molev, O. Yakimova, “Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras”, Represent. Theory, 23:12 (2019), 350–378 | DOI | MR

[9] 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

[10] Ya. Ikeda, “Kvazidifferentsialnyi operator i kvantovyi metod sdviga invariantov”, TMF, 212:1 (2022), 33–39 | DOI | DOI | MR

[11] Y. Ikeda, G. I. Sharygin, “The argument shift method in universal enveloping algebra $U\mathfrak{gl}_d$”, J. Geom. Phys., 195 (2024), 105030, 11 pp. | DOI | MR

[12] Y. Ikeda, A. Molev, G. Sharygin, On the quantum argument shift method, arXiv: 2309.15684