Geodesic
Reflection operator and hypergeometry II: $SL(2,\mathbb{C})$ spin chain
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 47-79

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We consider noncompact open $SL(2, \mathbb{C})$ spin chain and construct eigenfunctions of $B$-element of monodromy matrix for the simplest case of the chain with one site. The reflection operator appearing in this construction can be used to express eigenfunction for $n$ sites in terms of the eigenfunction for $n-1$ sites, this general result is briefly announced. We prove orthogonality and completeness of constructed eigenfunctions in the case of one site, express them in terms of the hypergeometric function of the complex field and derive the equation for the reflection operator with the general $SL(2,\mathbb{C})$-invariant $\mathbb{R}$-operator. 
@article{ZNSL_2024_532_a1,
     author = {P. V. Antonenko and N. M. Belousov and S. \`E. Derkachov and P. A. Valinevich},
     title = {Reflection operator and hypergeometry {II:} $SL(2,\mathbb{C})$ spin chain},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {47--79},
     publisher = {mathdoc},
     volume = {532},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a1/}
}
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P. V. Antonenko; N. M. Belousov; S. È. Derkachov; P. A. Valinevich. Reflection operator and hypergeometry II: $SL(2,\mathbb{C})$ spin chain. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 47-79. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a1/