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JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. POMI, 2023, Volume 520, Pages 50–123 (Mi znsl7313)

Baxter $Q$-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases
N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin

References

1. E. W. Barnes, “The theory of the double gamma function”, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 196 (1901), 265–387  mathscinet
2. N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin, Baxter operators in Ruijsenaars hyperbolic system I. Commutativity of $Q$-operators, arXiv: 2303.06383
3. N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin, Baxter operators in Ruijsenaars hyperbolic system II. Bispectral wave functions, arXiv: 2303.06382
4. L. D. Faddeev, “Discrete Heisenberg–Weyl Group and modular group”, Lett. Math. Phys., 34 (1995), 249–254  crossref  mathscinet  zmath
5. L. D. Faddeev, R. M. Kashaev, A. Yu. Volkov, “Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality”, Commun. Math. Phys., 219 (2001), 199–219  crossref  mathscinet  zmath
6. L. D. Faddeev, O. A. Yakubovsky, Lectures in Quantum Mechanics for Mathematician Students, Student Mathematical Library, 47, AMS, 2009  crossref  mathscinet
7. I. M. Gelfand, G. E. Shilov, Generalized Functions: Properties and operations, Academic Press, 1964  mathscinet  zmath
8. M. Hallnäs, S. Ruijsenaars, “Joint eigenfunctions for the relativistic Calogero–Moser Hamiltonians of hyperbolic type: I. First steps”, Int. Math. Res. Notices, 2014, 4400–4456  crossref  mathscinet  zmath
9. M. Hallnäs, S. Ruijsenaars, “A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians”, Int. Math. Res. Notices, 2015, 10278–10313  crossref  mathscinet  zmath
10. M. Hallnäs, S. Ruijsenaars, “Product formulas for the relativistic and nonrelativistic conical functions”, Adv. Stud. Pure Math., 76 (2018), 195–246  crossref  mathscinet
11. S. Kharchev, S. Khoroshkin, Wave function for $GL(n,\mathbb{R})$ hyperbolic Sutherland model, arXiv: 2108.04895
12. N. Kurokawa, S-Y. Koyama, “Multiple sine functions”, Forum Math., 15 (2003), 839–876  crossref  mathscinet  zmath
13. M. L. Nazarov, E. K. Sklyanin, “Sekiguchi–Debiard operators at infinity”, Commun. Math. Phys., 324 (2013), 831–849  crossref  mathscinet  zmath
14. M. L. Nazarov, E. K. Sklyanin, “Macdonald operators at infinity”, J. Algebraic Combin., 40 (2013), 23–44  crossref  mathscinet
15. B. Ponsot, J. Teschner, “Clebsch–Gordan and Racah–Wigner coefficients for a continuous series of representations of $ U_q (sl(2, \mathbb{R}))$”, Commun. Mathe. Phys., 224 (2001), 613–655  crossref  mathscinet
16. S. N. M. Ruijsenaars, “First-order analytic difference equations and integrable quantum systems”, J. Math. Phys., 38 (1997), 1069–1146  crossref  mathscinet  zmath
17. S. N. M. Ruijsenaars, “Zero-eigenvalue eigenfunctions for differences of elliptic relativistic Calogero–Moser Hamiltonians”, Theor. Math. Phys., 146:1 (2006), 25–33  mathnet  crossref  zmath


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