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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn062, 15 pages, doi:10.1093/imrn/rnn062 published on June 17, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Harish-Chandra Integrals as Nilpotent Integrals

Marco Bertola1,2 and Aleix Prats Ferrer2

1 Department of Mathematics and Statistics, Concordia University 1455 de Maisonneuve W., Montréal, Québec, Canada H3G 1M8
2 Centre de recherches mathématiques, Université de Montréal 2920 Chemin de la tour, Montréal, Québec, Canada H3T 1J4

Correspondence: Correspondence to be sent to: bertola{at}mathstat.concordia.ca

Recently, the correlation functions of the so-called Itzykson–Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact groups with respect to the Haar measure and Gaussian integrals over a maximal nilpotent Lie subalgebra of their complexification. Since the integration formula a posteriori had the same form for the classical series, a conjecture was formulated that such a formula should hold for arbitrary semisimple Lie groups. We prove this conjecture using an abstract Lie-theoretic approach.


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