$\mathrm{SL}(2,\mathbb{C})$ Gustafson integrals

Abstract

It was shown recently that many of the Gustafson integrals appear in studies of the $\mathrm{SL}(2,\mathbb{R})$ 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 $\mathrm{SL}(2,\mathbb{C})$ symmetry group and derive several new integrals