Harish-Chandra integrals as nilpotent integrals

Details Harish-Chandra integrals as nilpotent integrals Harish-Chandra integrals as nilpotent integrals

2008-01-22

arxiv.org/abs/0801.3452v1

Mathematics

Group Theory

10 pages

Scientific paper

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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