2007

The importance of the Selberg integral

Forrester, Peter J., Warnaar, S. Ole

Understand

It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name.

One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral.
We trace its sudden rise to prominence, initiated by a question to Selberg from Enrico Bombieri, more than thirty years after publication.
In quick succession the Selberg integral was used to prove an outstanding conjecture in random matrix theory, and cases of the Macdonald conjectures.

Built on

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Similar

E.M. Opdam, Some applications of hypergeometric shift operators
1989
Cited alongside, same era.
A. Selberg, Collected papers I
1989
Cited alongside, same era.
R.P. Stanley, Some combinatorial properties of Jack symmetric functions
1989
Cited alongside, same era.
D. Zeilberger, A Stembridge–Stanton style proof of the Habsieger–Kadell q q -Morris identity
1989
Cited alongside, same era.
G.W. Anderson, The evaluation of Selberg sums
1990
Cited alongside, same era.
F.G. Garvan, A proof of the Macdonald–Morris root system conjecture for F 4 F_{4}
1990
Cited alongside, same era.
R.A. Gustafson, A generalization of the Selberg beta-integral
1990
Cited alongside, same era.
A. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I
1990
Cited alongside, same era.
G.W. Anderson, A short proof of Selberg’s generalized beta formula
1991
Cited alongside, same era.
I.V. Cherednik, A unification of the Knizhnik–Zamolodchikov and Dunkl operators via affine Hecke algebras
1991
Cited alongside, same era.
R.J. Evans, The evaluation of Selberg character sums
1991
Cited alongside, same era.
F.G. Garvan and G. Gonnet, Macdonald’s constant term conjectures for exceptional root systems
1991
Cited alongside, same era.

Then

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1999
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