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@ARTICLE{Derkachov:436008,
      author       = {Derkachov, Sergey E. and Manashov, Alexander N.},
      title        = {{O}n {C}omplex {G}amma-{F}unction {I}ntegrals},
      journal      = {Symmetry, integrability and geometry: methods and
                      applications},
      volume       = {16},
      issn         = {1815-0659},
      address      = {[S.l.]},
      reportid     = {PUBDB-2020-00886, arXiv:1908.01530. DESY-19-116},
      pages        = {003},
      year         = {2020},
      note         = {publication: SIGMA 16 (2020) 003 ; ;},
      abstract     = {It 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.},
      keywords     = {spin: chain (INSPIRE) / higher-dimensional (INSPIRE) /
                      Hilbert space (INSPIRE) / magnet (INSPIRE) / semiclassical
                      (INSPIRE) / integrability (INSPIRE) / gauge field theory
                      (INSPIRE) / mathematical methods (INSPIRE) / SL(2,R)
                      (INSPIRE)},
      cin          = {UNI/TH},
      ddc          = {530},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {899 - ohne Topic (POF3-899)},
      pid          = {G:(DE-HGF)POF3-899},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)29 / PUB:(DE-HGF)16},
      eprint       = {1908.01530},
      howpublished = {arXiv:1908.01530},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1908.01530;\%\%$},
      UT           = {WOS:000511340800001},
      doi          = {10.3842/SIGMA.2020.003},
      url          = {https://bib-pubdb1.desy.de/record/436008},
}