An Arithmetic Invariant of the Jacquet-Langlands correspondence
Number Theory
2026-04-21 v5 Representation Theory
Abstract
We describe the local-global compatibility of local Plancherel measures and the Tamagawa measure under the Jacquet-Langlands correspondence. We apply the notion of densities of modules over a discrete group, which generalizes the dimensions over a discrete group. We prove that the global Jacquet-Langlands correspondence preserves the densities over principal arithmetic groups.
Keywords
Cite
@article{arxiv.2405.18372,
title = {An Arithmetic Invariant of the Jacquet-Langlands correspondence},
author = {Jun Yang},
journal= {arXiv preprint arXiv:2405.18372},
year = {2026}
}
Comments
This version has been shortened; the representation-theoretic and operator-algebraic content has been moved to arXiv:2503.13929 (published in Communications in Mathematical Physics, Volume 407, Article 100, 2026)