Geodesic
Mellin--Barnes representation for $SL(2, \mathbb{C})$ magnet
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 125-143

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We consider $SL(2, \mathbb{C})$ spin magnet and construct eigenfunctions for the element $A(u)$ of the monodromy matrix. We use recursive procedure which gives representations of these functions in the form of Mellin-Barnes type integrals. We compare these functions to those constructed earlier by S. Derkachov and A. Manashov (Gauss–Givental representation) and prove that they coincide up to normalization factor. 
@article{ZNSL_2020_494_a6,
     author = {P. A. Valinevich},
     title = {Mellin--Barnes representation for $SL(2, \mathbb{C})$ magnet},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--143},
     publisher = {mathdoc},
     volume = {494},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a6/}
}
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P. A. Valinevich. Mellin--Barnes representation for $SL(2, \mathbb{C})$ magnet. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 125-143. http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a6/