Hecke algebras and the Schlichting completion for discrete quantum groups

Skalski, A., Vergnioux, R. and Voigt, C. (2023) Hecke algebras and the Schlichting completion for discrete quantum groups. Journal of the London Mathematical Society, 107(3), pp. 843-885. (doi: 10.1112/jlms.12701)

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We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the construction of the Schlichting completion to the quantum setting, thus obtaining locally compact quantum groups with compact open quantum subgroups. We study in detail a class of examples arising from quantum HNN extensions.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Voigt, Professor Christian
Authors: Skalski, A., Vergnioux, R., and Voigt, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the London Mathematical Society
ISSN (Online):1469-7750
Published Online:07 December 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Journal of the London Mathematical Society 107(3): 843-885
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
309470Quantum groups in actionChristian VoigtEngineering and Physical Sciences Research Council (EPSRC)EP/T03064X/1M&S - Mathematics