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On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of D×
Abstract
We investigate the structure of locally analytic representations of p-adic groups, and establish a sufficient condition for the irreducibility of locally analytic vectors in certain Banach representations of D×, where D is the quaternion division algebra over ℚp. As an application, we prove that JL(ρ)an/JL(ρ)1−alg is a topologically irreducible locally analytic representation of D× under certain genericity conditions on ρ. Here JL(ρ) is the ρ(−1)-multiplicity space in the image of Π(ρ) under Scholze's functor, and Π(ρ) is the representation associated to ρ by the p-adic local Langlands correspondence.
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BibTeX
@misc{xiao2026irreducibility,
title = {{On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of $D^\times$}},
author = {Yu Xiao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04514},
eprint = {2611.04514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04514},
}
RIS
TY - UNPB
TI - On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of D^×
AU - Yu Xiao
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04514
UR - https://arxiv.org/abs/2611.04514
AB - We investigate the structure of locally analytic representations of p-adic groups, and establish a sufficient condition for the irreducibility of locally analytic vectors in certain Banach representations of D^×, where D is the quaternion division algebra over ℚ_p. As an application, we prove that JL(ρ)^an/JL(ρ)^1−alg is a topologically irreducible locally analytic representation of D^× under certain genericity conditions on ρ. Here JL(ρ) is the ρ(−1)-multiplicity space in the image of Π(ρ) under Scholze's functor, and Π(ρ) is the representation associated to ρ by the p-adic local Langlands correspondence.
ER -