Inversions of integral operators and elliptic beta integrals on root systems

By V. Spiridonov, S. Ole Warnaar. 2004

100 citations recorded by the source corpus.

We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type elliptic beta integrals, we obtain a new elliptic beta integral for the root system of type A. Validity of this integral is established by a different method as well.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e900960d45fc0e5289c0984c8ffcf0ed909d248a

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In Algebra and Number Theory

1. G. Vartanov
2. Shlomo S. Razamat
3. L. Rastelli
4. Abhijit Gadde
5. Wenbin Yan
6. E. Pomoni
7. V. Spiridonov
8. Eric M. Rains

In Applied Mathematics

1. G. Vartanov
2. Abhijit Gadde
3. Shlomo S. Razamat
4. L. Rastelli
5. Wenbin Yan
6. E. Pomoni
7. V. Spiridonov
8. Eric M. Rains

In Geometry and Topology

1. Abhijit Gadde
2. Wenbin Yan
3. Shlomo S. Razamat
4. G. Vartanov
5. L. Rastelli
6. V. Spiridonov
7. E. Pomoni
8. D. Gaiotto

Citations in the corpus

• Essays on the theory of elliptic hypergeometric functions (2008, methodology): “Different elliptic beta integrals on the root system An have been proposed in papers [11, 36].”
• Elliptic Hypergeometry of Supersymmetric Dualities (2009, methodology): “10) served as an entry ticket to the large class of new exactly computable integrals discussed in [19, 20, 21, 65, 83, 93], which is essentially extended by the conjectures presented in this paper.”
• S-duality and 2d topological QFT (2009, methodology): “y and use the results of the theory of elliptic Beta integrals to represent the deltafunction in a more elegant way, indeed such a representation is sometimes available in terms of a contour integral [34]. However, for generic choices of the parameters, the definition of [34] involves contour integra”
• N=1 theories of class S_k (2015, unknown): “transform [42], to obtain explicitly the index of the strongly coupled theory without using the eigenfunction.”
• The superconformal index of the E6 SCFT (2010, methodology): “Inversion theorem In this appendix we quote the inversion theorem [11], which we use in section 3.”