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2009 A Selberg integral for the Lie algebra An
S. Ole Warnaar
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Acta Math. 203(2): 269-304 (2009). DOI: 10.1007/s11511-009-0043-x


A new q-binomial theorem for Macdonald polynomials is employed to prove an An analogue of the celebrated Selberg integral. This confirms the $ \mathfrak{g} ={\rm{A}}_{n}$ case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra $ \mathfrak{g} $.

Funding Statement

Work supported by the Australian Research Council.


To the memory of Atle Selberg


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S. Ole Warnaar. "A Selberg integral for the Lie algebra An." Acta Math. 203 (2) 269 - 304, 2009.


Received: 4 September 2007; Published: 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1243.33053
MathSciNet: MR2570072
Digital Object Identifier: 10.1007/s11511-009-0043-x

Primary: 05E05
Secondary: 33C70 , 33D67

Keywords: Beta integrals , Macdonald polynomials , Selberg integrals

Rights: 2009 © Institut Mittag-Leffler

Vol.203 • No. 2 • 2009
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