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• W1975017574 abstract "We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BC_n and A_n; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BC_n, we also consider their “Type II” integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint integral operators; a different proof gives rise to pairs of adjoint difference operators. These allow us to construct a family of biorthogonal abelian functions generalizing the Koornwinder polynomials, and satisfying the analogues of the Macdonald conjectures. Finally, we discuss some transformations of Type II-style integrals. In particular, we find that adding two parameters to the Type II integral gives an integral invariant under an appropriate action of the Weyl group E_7." @default.
• W1975017574 created "2016-06-24" @default.
• W1975017574 creator A5060927791 @default.
• W1975017574 date "2010-03-17" @default.
• W1975017574 modified "2023-09-30" @default.
• W1975017574 title "Transformations of elliptic hypergeometric integrals" @default.
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• W1975017574 doi "https://doi.org/10.4007/annals.2010.171.169" @default.
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