Baxter operators in Ruijsenaars hyperbolic system I. Commutativity of Q-operators

2023/03/11 by N. Belousov, Belousov, N., S. Derkachov +5 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2303.06383

openalex publication_date 2023/03/11 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

We introduce Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. We prove that they represent a commuting family of integral operators and also commute with Macdonald difference operators, which are gauge equivalent to the Ruijsenaars Hamiltonians of the quantum system. The proof of commutativity of the Baxter operators uses a hypergeometric identity on rational functions that generalize Ruijsenaars kernel identities.

Cited by

• Baker-Akhiezer specialisation of joint eigenfunctions for hyperbolic relativistic Calogero-Moser Hamiltonians
• Calogero-Sutherland hyperbolic system and Heckman-Opdam \mathfrakgl_n hypergeometric function
• Complex rational Ruijsenaars model. The two-particle case
• BC-type open SL(2,ℂ) spin chain
• A-Type Open \rm SL(2,ℂ) Spin Chain

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