Geodesic
Transformations of elliptic hypergeometric integrals
Eric M. Rains1
1 Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, United States
Annals of mathematics, Tome 171 (2010) no. 1, pp. 169-243.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $E_7$.
DOI : 10.4007/annals.2010.171.169

Eric M. Rains 1

1 Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, United States 
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Eric M. Rains. Transformations of elliptic  hypergeometric integrals. Annals of mathematics, Tome 171 (2010) no. 1, pp. 169-243. doi : 10.4007/annals.2010.171.169. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.169/

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