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arXiv · 2505.04355

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

Sascha Orlik
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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.

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Sascha Orlik. 2025-05-07. On some non-principal locally analytic representations induced by cuspidal Lie algebra representations. https://arxiv.org/abs/2505.04355

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