Adelic C*-correspondences and parabolic induction
Operator Algebras
2026-01-13 v2 Representation Theory
Abstract
In analogy with the construction of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert C*-modules and of C*-correspondences. The construction produces global C*-correspondences from compatible collections of local C*-correspondences. When applied to the collection of C*-correspondences capturing local parabolic induction, the construction produces a global C*-correspondence that captures adelic parabolic induction.
Keywords
Cite
@article{arxiv.2412.02379,
title = {Adelic C*-correspondences and parabolic induction},
author = {Magnus Goffeng and Bram Mesland and Mehmet Haluk Sengun},
journal= {arXiv preprint arXiv:2412.02379},
year = {2026}
}
Comments
Several improvements, especially in Section 6, following referee's suggestions. To appear in the Journal of Functional Analysis