Transformations of elliptic hypergometric integrals

Details Transformations of elliptic hypergometric integrals Transformations of elliptic hypergometric integrals

2003-09-16

arxiv.org/abs/math/0309252v4

Mathematics

Quantum Algebra

58 pages, LaTeX. v2: some notations changed to harmonize with sequel. v3: added proof of main conjecture; other minor changes.

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Transformations of elliptic hypergometric integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transformations of elliptic hypergometric integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transformations of elliptic hypergometric integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-690664