Geodesic
Reflection operator and hypergeometry I: $SL(2,\mathbb{R})$ spin chain
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 5-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Reflection operator and hypergeometry {I:} $SL(2,\mathbb{R})$ spin chain},
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P. V. Antonenko; N. M. Belousov; S. È. Derkachov; S. M. Khoroshkin. Reflection operator and hypergeometry I: $SL(2,\mathbb{R})$ spin chain. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 5-46. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a0/

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