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arXiv · 2406.19862

Reflection operator and hypergeometry I: $SL(2, \mathbb{R})$ spin chain

P. Antonenko·N. Belousov·S. Derkachov·S. Khoroshkin
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Abstract

In this work we consider open $SL(2, \mathbb{R})$ spin chain, mainly the simplest case of one particle. Eigenfunctions of the model can be constructed using the so-called reflection operator. We obtain several representations of this operator and show its relation to the hypergeometric function. Besides, we prove orthogonality and completeness of one-particle eigenfunctions and connect them to the index hypergeometric transform. Finally, we briefly state the formula for the eigenfunctions in many-particle case.

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P. Antonenko, N. Belousov, S. Derkachov, S. Khoroshkin. 2024-06-28. Reflection operator and hypergeometry I: $SL(2, \mathbb{R})$ spin chain. https://arxiv.org/abs/2406.19862

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