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An elliptic hypergeometric integral with W(F_4) symmetry · Around

2009

An elliptic hypergeometric integral with W(F_4) symmetry

van de Bult, Fokko J.

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In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F_4.

The transformation is a generalization of a series transformation discovered by Langer, Schlosser, and Warnaar.
Moreover we consider various limits of this transformation to basic hypergeometric functions obtained by letting p tend to 0.

Built on

J.E. Humphreys, Reflection Groups and Coxeter Groups
1990
Earlier work this paper cites.
I.B. Frenkel and V.G. Turaev, Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
1997
Earlier work this paper cites.
V.P. Spiridonov, On the elliptic beta function
2001
Earlier work this paper cites.

Similar

G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Vol. 96, 2nd ed., Cambridge University Press, Cambridge, 2004
2004
Cited alongside, same era.
V.P. Spiridonov, Theta hypergeometric integrals
2004
Cited alongside, same era.
F.J. van de Bult and E.M. Rains, Basic hypergeometric functions as limits of elliptic hypergeometric functions
Original
2009
Cited alongside, same era.

Then

R. Langer, M.J. Schlosser and S.O. Warnaar, Theta Functions, Elliptic Hypergeometric Series, and Kawanaka’s Macdonald Polynomial Conjecture
Original
2009
Closest in time.
E.M. Rains, Transformations of elliptic hypergeometric integrals
2009
Closest in time.

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