N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin, “Baxter <nobr>$Q$</nobr>-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases”, Zap. Nauchn. Sem. POMI, 2023, Volume 520,Pages <nobr>50

Baxter $Q$-operators in Ruijsenaars–Sutherland hyperbolic systems: one- and two-particle cases

N. Belousov^a, S. Derkachov^a, S. Kharchev^bc, S. Khoroshkin^cd

^a Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia
^b National Research Center “Kurchatov Institute”
^c Institute for Information Transmission Problems RAS (Kharkevich Institute), Bolshoy Karetny per. 19, Moscow, 127994, Russia
^d National Research University Higher School of Economics

Abstract: In these notes we review the technique of Baxter $Q$-operators in the Ruijsenaars-Sutherland hyperbolic systems in the cases of one and two particles. Using these operators we show in particular that eigenfunctions of these systems admit two dual integral representations and prove their orthogonality and completeness.

Key words and phrases: Ruijsenaars, Sutherland, Calogero, Baxter $Q$-operator, eigenfunctions, orthogonality, completeness.

UDC: 517

Received: 03.07.2023

Language: English