# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc: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
@inproceedings{s.2007a,
title={A Selberg integral for the Lie algebra A_{$n$}},
author={S. Ole Warnaar},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203354485952719},
booktitle={Acta Mathematica},
volume={203},
number={2},
pages={269-304},
year={2007},
}

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.