Abstract
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.
Note
To the memory of Atle Selberg
Citation
S. Ole Warnaar. "A Selberg integral for the Lie algebra An." Acta Math. 203 (2) 269 - 304, 2009. https://doi.org/10.1007/s11511-009-0043-x
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