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Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains

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arxiv 2102.13570 v2 pith:WN4R4P4Y submitted 2021-02-26 math-ph hep-thmath.MPnlin.SI

Sergey É. Derkachov , Karol K. Kozlowski , Alexander N. Manashov This is my paper · ORCID
classification math-phhep-thmath.MPnlin.SI
keywords chainsintegralsmathbbmathrmspinallowingcasecompleteness
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abstract

This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite-dimensional representations of rank one quantum integrable models. We examine in detail the case of the $\mathrm{SL}(2,\mathbb R)$ spin chains.

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  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.

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