On some non-principal locally analytic representations induced by cuspidal Lie algebra representations

Sascha Orlik

On some non-principal locally analytic representations induced by cuspidal Lie algebra representations

Representation Theory 2026-05-06 v3 Number Theory

Authors: Sascha Orlik

Abstract

Let $G$ be a split reductive $p$ -adic Lie group. This paper is the first in a series on the construction of locally analytic $G$ -representations which do not lie in the principal series. Here we consider the case of the general linear group $G=GL_{n+1}$ and locally analytic representations which are induced by cuspidal modules of the Lie algebra. We prove that they are ind-admissible and satisfy the homological vanishing criterion in the definition of supercuspidality in the sense of Kohlhaase.

Keywords

locally analytic representations split reductive p-adic Lie group cuspidal Lie algebra representations ind-admissible supercuspidality homological vanishing criterion

Cite

@article{arxiv.2505.04355,
  title  = {On some non-principal locally analytic representations induced by cuspidal Lie algebra representations},
  author = {Sascha Orlik},
  journal= {arXiv preprint arXiv:2505.04355},
  year   = {2026}
}

Comments

with an appendix by Andreas Bode, version 2: Minor changes and Prop. 6.1 was fixed. Version 3: Correction to Theorem B and new appendix

On some non-principal locally analytic representations induced by cuspidal Lie algebra representations

Abstract

Keywords

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