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arXiv · 2203.01166

Hecke algebras and the Schlichting completion for discrete quantum groups

Adam Skalski·Roland Vergnioux·Christian Voigt
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Abstract

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.

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Adam Skalski, Roland Vergnioux, Christian Voigt. 2022-03-02. Hecke algebras and the Schlichting completion for discrete quantum groups. https://doi.org/10.1112/jlms.12701

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