15 August 2002 Hua-type integrals over unitary groups and over projective limits of unitary groups
Yurii A. Neretin
Duke Math. J. 114(2): 239-266 (15 August 2002). DOI: 10.1215/S0012-7094-02-11423-9

Abstract

We discuss some natural maps from a unitary group ${\rm U}(n)$ to a smaller group ${\rm U}(n-m)$. (These maps are versions of the Livšic characteristic function.) We calculate explicitly the direct images of the Haar measure under some maps. We evaluate some matrix integrals over classical groups and some symmetric spaces. (Values of the integrals are products of $\Gamma$-functions.) These integrals generalize Hua integrals. We construct inverse limits of unitary groups equipped with analogues of Haar measure and evaluate some integrals over these inverse limits.

Citation

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Yurii A. Neretin. "Hua-type integrals over unitary groups and over projective limits of unitary groups." Duke Math. J. 114 (2) 239 - 266, 15 August 2002. https://doi.org/10.1215/S0012-7094-02-11423-9

Information

Published: 15 August 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1019.43008
MathSciNet: MR1920189
Digital Object Identifier: 10.1215/S0012-7094-02-11423-9

Subjects:
Primary: 43A85

Rights: Copyright © 2002 Duke University Press

Vol.114 • No. 2 • 15 August 2002
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