Gustafson integrals for $SL(2,\mathbb{C})$ spin magnet
  It was observed recently that the multidimensional Mellin--Barnes integrals (Gustafson's integrals) arise naturally in studies of the $SL(2,R)$ spin chain models. We extend this analysis to the noncompact $SL(2,\mathbb{C})$ spin magnets and obtain integrals which generalize Gustafson's integrals to the complex case. 
S.E. Derkachov, A.N. Manashov, P.A. Valinevich
math-ph hep-th math.MP