A Selberg integral for the Lie algebra A_n

A Lascoux; A Selberg; A Varchenko; A Varchenko; A Varchenko; CF Dunkl; E Mukhin; EM Opdam; EM Opdam; FG Garvan; G Gasper; GE Andrews; IG Macdonald; IG Macdonald; J Kaneko; J Kaneko; J Thomae; K Aomoto; K Mimachi; KWJ Kadell; L Euler; ML Mehta; PI Etingof; PJ Forrester; R Askey; RP Stanley; S. Ole Warnaar; SO Warnaar; TH Baker; V Tarasov; VV Schechtman

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A Selberg integral for the Lie algebra A_n

Authors: A Lascoux
A Selberg
A Varchenko
A Varchenko
A Varchenko
CF Dunkl
E Mukhin
EM Opdam
EM Opdam
FG Garvan
G Gasper
GE Andrews
IG Macdonald
IG Macdonald
J Kaneko
J Kaneko
J Thomae
K Aomoto
K Mimachi
KWJ Kadell
L Euler
ML Mehta
PI Etingof
PJ Forrester
R Askey
RP Stanley
S. Ole Warnaar
SO Warnaar
TH Baker
V Tarasov
VV Schechtman
Publication date: 8 August 2007
Publisher: 'Springer Science and Business Media LLC'
Doi

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 g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

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