A Mackey criterion for locally analytic representations

Andreas Bode

A Mackey criterion for locally analytic representations

Number Theory 2026-07-03 v1 Representation Theory

Authors: Andreas Bode

Abstract

We prove an analogue of Mackey's irreducibility criterion for compactly induced locally analytic representations of $p$ -adic groups, where we induce from an open subgroup which is compact mod centre. We also discuss several examples.

Cite

@article{arxiv.2607.02976,
  title  = {A Mackey criterion for locally analytic representations},
  author = {Andreas Bode},
  journal= {arXiv preprint arXiv:2607.02976},
  year   = {2026}
}

Comments

22 pages, comments welcome. This paper was first conceived as an appendix to arXiv:2505.04355, before we realized that the correct formulation of the criterion does not apply there. This is now an updated and expanded version, including several new examples