A Selberg integral for the Lie algebra A_{$n$}

S. Ole Warnaar School of Mathematics and Physics, The University of Queensland

TBD mathscidoc:1701.332010

Acta Mathematica, 203, (2), 269-304, 2007.9
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} $ .
Beta integrals; Selberg integrals; Macdonald polynomials
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  title={A Selberg integral for the Lie algebra A_{$n$}},
  author={S. Ole Warnaar},
  booktitle={Acta Mathematica},
S. Ole Warnaar. A Selberg integral for the Lie algebra A_{$n$}. 2007. Vol. 203. In Acta Mathematica. pp.269-304. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203354485952719.
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