SL(2, C) Gustafson Integrals

Abstract

It was shown recently that many of the Gustafson integrals appear in studies of the SL(2, 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 SL(2, C) symmetry group in the case of open and periodic boundary conditions and derive several new integrals.