Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-12T08:32:32.601Z Has data issue: false hasContentIssue false

IDENTIFICATION OF THE POISSON AND MARTIN BOUNDARIES OF ORTHOGONAL DISCRETE QUANTUM GROUPS

Published online by Cambridge University Press:  16 November 2007

Stefaan Vaes
Affiliation:
CNRS, Institut de Mathématiques de Jussieu, Algèbres d'Opérateurs, 175, rue du Chevaleret, F-75013 Paris, France Katholieke Universiteit Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium (stefaan.vaes@wis.kuleuven.be; nikolas.vandervennet@wis.kuleuven.be)
Nikolas Vander Vennet
Affiliation:
Katholieke Universiteit Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium (stefaan.vaes@wis.kuleuven.be; nikolas.vandervennet@wis.kuleuven.be)

Abstract

The Poisson and Martin boundaries for invariant random walks on the dual of the orthogonal quantum groups $A_{\mathrm{o}}(F)$ are identified with higher-dimensional Podleś spheres that we describe in terms of generators and relations. This provides the first such identification for random walks on non-amenable discrete quantum groups.

Type
Research Article
Copyright
2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)