A specific limit of the star-star relation produces the flipping relation, and new flipping solutions are given in several gamma-function families.
Gamma function solutions to the star-triangle equation
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In the paper, we clarify some relations between solutions to the star-triangle equation via the gauge/YBE correspondence. We consider two solutions to the star-triangle relation in terms of Euler's gamma function. We derive these solutions from the reduction of certain basic and hyperbolic hypergeometric integral identities. These identities can be interpreted as equality of the supersymmetric partition functions of a specific three-dimensional N=2 supersymmetric dual theories.
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Flipping relation as a reduced star-star relation
A specific limit of the star-star relation produces the flipping relation, and new flipping solutions are given in several gamma-function families.