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A Selberg integral for the Lie algebra A n

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Acta Mathematica

Abstract

A new q-binomial theorem for Macdonald polynomials is employed to prove an A n 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 \( \mathfrak{g} \).

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Authors and Affiliations

  1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia

    S. Ole Warnaar

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  1. S. Ole Warnaar
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Correspondence to S. Ole Warnaar.

Additional information

To the memory of Atle Selberg

Work supported by the Australian Research Council.

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Warnaar, S.O. A Selberg integral for the Lie algebra A n . Acta Math 203, 269–304 (2009). https://doi.org/10.1007/s11511-009-0043-x

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  • DOI: https://doi.org/10.1007/s11511-009-0043-x

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