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

Published online by Cambridge University Press:  16 November 2007

Stefaan Vaes  and
Nikolas Vander Vennet
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)
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Abstract

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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.

Keywords

quantum random walkPoisson boundaryMartin boundarydiscrete quantum groupcompact quantum groupmonoidal equivalencePrimary 46L5360J5016W30
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 2 , April 2008 , pp. 391 - 412
Copyright
2007 Cambridge University Press