TY  - JOUR
AU  - Derkachov, Sergey E.
AU  - Manashov, Alexander N.
TI  - On Complex Gamma-Function Integrals
JO  - Symmetry, integrability and geometry: methods and applications
VL  - 16
IS  - arXiv:1908.01530
SN  - 1815-0659
CY  - [S.l.]
M1  - PUBDB-2020-00886
M1  - arXiv:1908.01530
M1  - DESY-19-116
SP  - 003
PY  - 2020
N1  - publication: SIGMA 16 (2020) 003 ; ;
AB  - It was observed recently that relations between matrix elements of certain operators in the SL(2,\mathbb R) spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with SL(2,\mathbb C) symmetry group and L<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 (INSPIRE)
KW  - higher-dimensional (INSPIRE)
KW  - Hilbert space (INSPIRE)
KW  - magnet (INSPIRE)
KW  - semiclassical (INSPIRE)
KW  - integrability (INSPIRE)
KW  - gauge field theory (INSPIRE)
KW  - mathematical methods (INSPIRE)
KW  - SL(2,R) (INSPIRE)
LB  - PUB:(DE-HGF)29 ; PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000511340800001
DO  - DOI:10.3842/SIGMA.2020.003
UR  - https://bib-pubdb1.desy.de/record/436008
ER  -