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arXiv · 1908.01530

On Complex Gamma-Function Integrals

Sergey E. Derkachov·Alexander N. Manashov
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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.

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Sergey E. Derkachov, Alexander N. Manashov. 2019-08-05. On Complex Gamma-Function Integrals. https://doi.org/10.3842/sigma.2020.003

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