Transformations of elliptic hypergometric integrals

By Eric M. Rains. 2003

47 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/45f6f73cc85582e381aad8ba3573387c33e7c5e6

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In Algebra and Number Theory

In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Short proofs of the elliptic beta integrals (2004, methodology): “rmally as a Dn integral). These are all elliptic beta integrals found so far. The ﬁrst complete proofs of the multiparameter Cn integral of [3] and An integral of [10] were obtained recently by Rains [8]. The present paper describes elementary proofs of these exact integration formulas modelled alon”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “Such identities were discovered by Rains from a purely mathematical perspective [35].”