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Baxter operators in Ruijsenaars hyperbolic system I. Commutativity of Q-operators
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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.
Forward citations
Cited by 3 Pith papers
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Ruijsenaars spectral transform
The Ruijsenaars spectral transform, a many-variable Fourier generalization, is claimed to have an inversion formula for complex parameters and to be unitary in four parameter regimes.
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A basic triad in Macdonald theory
At t=q^{-m}, the Noumi-Shiraishi series reproduces the Baker-Akhiezer function, completing a triad with the Macdonald polynomials.
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Chalykh's Baker-Akhiezer functions as eigenfunctions of the integer-ray integrable systems
In explicit small cases, twisted Baker-Akhiezer functions satisfy the defining linear equations and are eigenfunctions of the integer-ray DIM Hamiltonians.
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