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On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models

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arxiv 1806.04487 v1 pith:LQHJ42AM submitted 2018-06-12 math-ph hep-thmath.MPnlin.SI

classification math-phhep-thmath.MPnlin.SI
keywords latticemagnetmodularprovesinh-gordonallowinganalysisboldsymbol
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abstract

We construct the generalised Eigenfunctions of the entries of the monodromy matrix of the $N$-site modular XXZ magnet and show, in each case, that these form a complete orthogonal system in $L^2(\mathbb{R}^N)$. In particular, we develop a new and simple technique, allowing one to prove the completeness of such systems. As a corollary of out analysis, we prove the Bystko-Teschner conjecture relative to the structure of the spectrum of the $\boldsymbol{ \texttt{B} }(\la)$-operator for the odd length lattice Sinh-Gordon model.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ruijsenaars spectral transform

    math-ph 2024-11 reject novelty 6.0 of 10

    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.

  2. On Complex Gamma-Function Integrals

    math-ph 2019-08 conditional novelty 6.0 of 10

    Two complex gamma-function integral identities are proved directly and shown to imply star-triangle relations and the Dotsenko-Fateev duality in a classical limit.

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