Reflection operator and hypergeometry I: $SL(2, \mathbb{R})$ spin chain
Mathematical Physics
2024-07-09 v1 High Energy Physics - Theory
math.MP
Representation Theory
Exactly Solvable and Integrable Systems
Abstract
In this work we consider open 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.
Cite
@article{arxiv.2406.19862,
title = {Reflection operator and hypergeometry I: $SL(2, \mathbb{R})$ spin chain},
author = {P. Antonenko and N. Belousov and S. Derkachov and S. Khoroshkin},
journal= {arXiv preprint arXiv:2406.19862},
year = {2024}
}