Transformations of elliptic hypergometric integrals
| dc.creator | Rains, Eric M. | |
| dc.date | 2003-09-16 | |
| dc.date | 2005-04-20 | |
| dc.date.accessioned | 2026-07-07T05:01:08Z | |
| dc.date.available | 2026-07-07T05:01:08Z | |
| dc.description | 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. | |
| dc.description | 58 pages, LaTeX. v2: some notations changed to harmonize with sequel. v3: added proof of main conjecture; other minor changes. v4: appendix on meromorphy added | |
| dc.identifier | https://arxiv.org/abs/math/0309252 | |
| dc.identifier | http://arxiv.org/abs/math/0309252 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68571 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.title | Transformations of elliptic hypergometric integrals | |
| dc.type | text |