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.

Harish-Chandra Integrals as Nilpotent Integrals / Bertola, M.; Ferrer, A. P.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2008:(2008), pp. 1-15. [10.1093/imrn/rnn062]

Harish-Chandra Integrals as Nilpotent Integrals

Bertola, M.;
2008-01-01

Abstract

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.
2008
2008
1
15
rnn062
https://academic.oup.com/imrn/article/doi/10.1093/imrn/rnn062/701227
Bertola, M.; Ferrer, A. P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11345
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