Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 030, 16 pages      arXiv:1711.07822      https://doi.org/10.3842/SIGMA.2018.030
Contribution to the Special Issue on Elliptic Hypergeometric Functions and Their Applications

${\rm SL}(2,\mathbb{C})$ Gustafson Integrals

Sergey É. Derkachov a, Alexander N. Manashov abc and Pavel A. Valinevich a
a) Saint-Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
b) Institut für Theoretische Physik, Universität Hamburg, D-22761 Hamburg, Germany
c) Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany

Received January 19, 2018, in final form March 24, 2018; Published online March 31, 2018

Abstract
It was shown recently that many of the Gustafson integrals appear in studies of the ${\rm SL}(2,\mathbb{R})$ spin chain models. One can hope to obtain a generalization of the Gustafson integrals considering spin chain models with a different symmetry group. In this paper we analyse the spin magnet with the ${\rm SL}(2,\mathbb{C})$ symmetry group in case of open and periodic boundary conditions and derive several new integrals.

Key words: Baxter operators; separation of variables.

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