000436008 001__ 436008 000436008 005__ 20250803051602.0 000436008 0247_ $$2doi$$a10.3842/SIGMA.2020.003 000436008 0247_ $$2INSPIRETeX$$aDerkachov:2019ynh 000436008 0247_ $$2inspire$$ainspire:1747923 000436008 0247_ $$2arXiv$$aarXiv:1908.01530 000436008 0247_ $$2datacite_doi$$a10.3204/PUBDB-2020-00886 000436008 0247_ $$2WOS$$aWOS:000511340800001 000436008 0247_ $$2openalex$$aopenalex:W2964380902 000436008 0247_ $$2altmetric$$aaltmetric:64606947 000436008 037__ $$aPUBDB-2020-00886 000436008 041__ $$aEnglish 000436008 082__ $$a530 000436008 0881_ $$aarXiv:1908.01530; DESY-19-116 000436008 088__ $$2arXiv$$aarXiv:1908.01530 000436008 088__ $$2DESY$$aDESY-19-116 000436008 1001_ $$0P:(DE-HGF)0$$aDerkachov, Sergey E.$$b0$$eCorresponding author 000436008 245__ $$aOn Complex Gamma-Function Integrals 000436008 260__ $$a[S.l.]$$c2020 000436008 3367_ $$2DRIVER$$aarticle 000436008 3367_ $$2DataCite$$aOutput Types/Journal article 000436008 3367_ $$0PUB:(DE-HGF)29$$2PUB:(DE-HGF)$$aReport$$mreport 000436008 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1582711606_19362 000436008 3367_ $$2BibTeX$$aARTICLE 000436008 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000436008 3367_ $$00$$2EndNote$$aJournal Article 000436008 500__ $$apublication: SIGMA 16 (2020) 003 ; ; 000436008 520__ $$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. 000436008 536__ $$0G:(DE-HGF)POF3-899$$a899 - ohne Topic (POF3-899)$$cPOF3-899$$fPOF III$$x0 000436008 588__ $$aDataset connected to CrossRef, INSPIRE 000436008 650_7 $$2INSPIRE$$aspin: chain 000436008 650_7 $$2INSPIRE$$ahigher-dimensional 000436008 650_7 $$2INSPIRE$$aHilbert space 000436008 650_7 $$2INSPIRE$$amagnet 000436008 650_7 $$2INSPIRE$$asemiclassical 000436008 650_7 $$2INSPIRE$$aintegrability 000436008 650_7 $$2INSPIRE$$agauge field theory 000436008 650_7 $$2INSPIRE$$amathematical methods 000436008 650_7 $$2INSPIRE$$aSL(2,R) 000436008 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0 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. 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