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000436008 1001_ $$0P:(DE-HGF)0$$aDerkachov, Sergey E.$$b0$$eCorresponding author
000436008 245__ $$aOn Complex Gamma-Function Integrals
000436008 260__ $$a[S.l.]$$c2020
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000436008 520__ $$aIt was observed recently that relations between matrix elements of certain operators in the ${\rm SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with ${\rm SL}(2,\mathbb C)$ symmetry group and ${\rm L}_2(\mathbb C)$ as a local Hilbert space give rise to a new type of $\Gamma$-function integrals. In this work we present a direct calculation of two such integrals. We also analyse properties of these integrals and show that they comprise the star-triangle relations recently discussed in the literature. It is also shown that in the quasi-classical limit these integral identities are reduced to the duality relations for Dotsenko-Fateev integrals.
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000436008 7001_ $$0P:(DE-H253)PIP1024579$$aManashov, Alexander N.$$b1$$eCorresponding author
000436008 773__ $$0PERI:(DE-600)2205586-1$$a10.3842/SIGMA.2020.003$$p003$$tSymmetry, integrability and geometry: methods and applications$$v16$$x1815-0659$$y2020
000436008 7870_ $$0PUBDB-2019-03039$$aDerkachov, S. E. et.al.$$d2019$$iIsParent$$rarXiv:1908.01530; DESY-19-116$$tOn complex Gamma function integrals
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