Polynomial forms for quantum elliptic Calogero–Moser Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 1, pp. 14-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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We hypothesize the form of a transformation reducing the elliptic $A_N$ Calogero–Moser operator to a differential operator with polynomial coefficients. We verify this hypothesis for $N\le3$ and, moreover, give the corresponding polynomial operators explicitly.
Keywords: elliptic Calogero–Moser Hamiltonian, universal enveloping algebra.
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     author = {M. G. Matushko and V. V. Sokolov},
     title = {Polynomial forms for quantum elliptic {Calogero{\textendash}Moser} {Hamiltonians}},
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M. G. Matushko; V. V. Sokolov. Polynomial forms for quantum elliptic Calogero–Moser Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 1, pp. 14-24. http://geodesic.mathdoc.fr/item/TMF_2017_191_1_a1/

[1] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, v. 2, Fizmatlit, M., 1963 | DOI | MR | Zbl

[2] V. V. Sokolov, A. V. Turbiner, “Quasi-exact-solvability of the $A_{2}/G_2$ elliptic model: algebraic form, $sl(3)/g^{(2)}$ hidden algebra, and polynomial eigenfunctions”, J. Phys. A: Math. Theor., 48:15 (2015), 155201, 15 pp., arXiv: 1409.7439 | DOI | MR | Zbl

[3] W. Rühl, A. V. Turbiner, “Exact solvability of the Calogero and Sutherland models”, Modern Phys. Lett. A, 10:29 (1995), 2213–2222 | DOI | MR

[4] G. Post, N. van den Hijligenberg, “$gl(\lambda)$ and differential operators preserving polynomials”, Acta Appl. Math., 44:1–2 (1996), 257–268 | DOI | MR | Zbl

[5] R. P. Stanley, Enumerative Combinatorics, v. 2, Cambridge Univ. Press, Cambridge, 1997 | DOI | MR | Zbl

[6] H. Awata, Y. Matsuo, S. Odake, J. Shiraishi, “Collective field theory, Calogero–Sutherland model and generalized matrix models”, Phys. Lett. B, 347:1 (1995), 49–55 | DOI | MR | Zbl

[7] A. N. Sergeev, A. P. Veselov, “Dunkl operators at infinity and Calogero–Moser systems”, Internat. Math. Res. Notices, 2015:21, 10959–10986, arXiv: 1311.0853 | DOI | MR | Zbl