Two complex gamma-function integral identities are proved directly and shown to imply star-triangle relations and the Dotsenko-Fateev duality in a classical limit.
Spin Chains and Gustafson's Integrals
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abstract
Gustafson's integrals are multidimensional generalizations of the classical Mellin-Barnes integrals. We show that some of these integrals arise from relations between matrix elements in Sklyanin's representation of Separated Variables in spin chain models. We also present several new integrals.
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On Complex Gamma-Function Integrals
Two complex gamma-function integral identities are proved directly and shown to imply star-triangle relations and the Dotsenko-Fateev duality in a classical limit.