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Finite Length of Locally Analytic Vectors for GL2(F) and DF×
Abstract
Let F/Qp and E/Qp be finite extensions, and let G=GL2(F) or DF×, where DF is the quaternion division algebra over F. Let Π be an admissible Banach E-representation of G whose locally Qp-analytic vectors Πan have an infinitesimal character. If p>2 or F=Qp, we prove that Πan and Π have finite length in their respective admissible categories.
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BibTeX
@misc{ding2026finite,
title = {{Finite Length of Locally Analytic Vectors for $\mathrmGL_2(F)$ and $D_F^\times$}},
author = {Pengcheng Ding},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15841},
eprint = {2610.15841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15841},
}
RIS
TY - UNPB
TI - Finite Length of Locally Analytic Vectors for GL_2(F) and D_F^×
AU - Pengcheng Ding
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15841
UR - https://arxiv.org/abs/2610.15841
AB - Let F/Q_p and E/Q_p be finite extensions, and let G=GL_2(F) or D_F^×, where D_F is the quaternion division algebra over F. Let Π be an admissible Banach E-representation of G whose locally Q_p-analytic vectors Π^an have an infinitesimal character. If p>2 or F=Q_p, we prove that Π^an and Π have finite length in their respective admissible categories.
ER -