Weingarten integration over noncommutative homogeneous spaces
Annales mathématiques Blaise Pascal, Volume 24 (2017) no. 2, pp. 195-224.

We discuss an extension of the Weingarten formula, to the case of noncommutative homogeneous spaces, under suitable “easiness” assumptions. The spaces that we consider are noncommutative algebraic manifolds, generalizing the spaces of type X=G/H N , with HGU N being subgroups of the unitary group, subject to certain uniformity conditions. We discuss various axiomatization issues, then we establish the Weingarten formula, and we derive some probabilistic consequences.

On présente une extension de la formule d’intégration de Weingarten, pour les espaces homogènes non commutatifs, vérifiant des hypothèses « d’aisance » adéquates. Les espaces qu’on considère sont des variétés algebriques non commutatives, généralisant les espaces du type X=G/H N , avec HGU N étant des sous-groupes du groupe unitaire, vérifiant certaines conditions d’uniformité. On traite d’abord les questions d’axiomatisation, ensuite on établit la formule de Weingarten, et on finit avec quelques conséquences probabilistes.

Published online:
DOI: 10.5802/ambp.368
Classification: 46L51,  14A22,  60B15
Keywords: Noncommutative manifold, Weingarten integration
Teodor Banica 1

1 Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Teodor Banica. Weingarten integration over noncommutative homogeneous spaces. Annales mathématiques Blaise Pascal, Volume 24 (2017) no. 2, pp. 195-224. doi : 10.5802/ambp.368. https://ambp.centre-mersenne.org/articles/10.5802/ambp.368/

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