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.
On BC type basic hypergeometric orthogonal polynomials
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abstract
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain is given for which the partially discrete orthogonality measure is positive. The orthogonality relations and norm evaluations for multivariable q-Racah polynomials and multivariable big and little q-Jacobi polynomials are proved by taking suitable limits in the orthogonality relations for the multivariable Askey-Wilson polynomials. In particular new proofs of several well known q-analogues of the Selberg integral are obtained.
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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.