TY - EJOUR AU - Derkachov, S. E. AU - Manashov, A. N. TI - On complex Gamma function integrals IS - arXiv:1908.01530 M1 - PUBDB-2019-03039 M1 - arXiv:1908.01530 M1 - DESY-19-116 PY - 2019 AB - It was observed recently that relations between matrix elements of certain operators in the \textSL(2,\mathbb R) spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with \textSL(2,\mathbb C) symmetry group and \textL<sub>2</sub>(\mathbb C) as a local Hilbert space give rise to a new type of Γ-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. KW - spin: chain (autogen) KW - higher-dimensional (autogen) KW - Hilbert space (autogen) KW - duality (autogen) KW - magnet (autogen) LB - PUB:(DE-HGF)25 ; PUB:(DE-HGF)29 DO - DOI:10.3204/PUBDB-2019-03039 UR - https://bib-pubdb1.desy.de/record/424726 ER -