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@ARTICLE{Derkachov:424726,
      author       = {Derkachov, S. E. and Manashov, A. N.},
      title        = {{O}n complex {G}amma function integrals},
      reportid     = {PUBDB-2019-03039, arXiv:1908.01530. DESY-19-116},
      year         = {2019},
      abstract     = {It was observed recently that relations between matrix
                      elements of certain operators in the $\text{SL}(2,\mathbb
                      R)$ spin chain models take the form of multidimensional
                      integrals derived by R.A. Gustafson. The spin magnets with
                      $\text{SL}(2,\mathbb C)$ symmetry group and
                      $\text{L}_2(\mathbb C)$ 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.},
      keywords     = {spin: chain (autogen) / higher-dimensional (autogen) /
                      Hilbert space (autogen) / duality (autogen) / magnet
                      (autogen)},
      cin          = {UNI/TH},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {611 - Fundamental Particles and Forces (POF3-611)},
      pid          = {G:(DE-HGF)POF3-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25 / PUB:(DE-HGF)29},
      eprint       = {1908.01530},
      howpublished = {arXiv:1908.01530},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1908.01530;\%\%$},
      doi          = {10.3204/PUBDB-2019-03039},
      url          = {https://bib-pubdb1.desy.de/record/424726},
}