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On unitary representations of p-adic Sp2n and SO2n+1 of purely bad parity
Abstract
Let G be Sp2n(F) or split SO2n+1(F) over a non-archimedean local field F of characteristic zero. We classify the irreducible unitary representations of G of purely bad parity: such a representation is unitary if and only if it is of Arthur type, except for one additional family when G=Sp2n(F). In particular, we confirm the remaining case of Ciubotaru's conjecture for SO2n+1(F), namely that every unitary unipotent representation with integral infinitesimal parameter is of Arthur type.
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BibTeX
@misc{lo2026unitary,
title = {{On unitary representations of $p$-adic $\textrmSp_2n$ and $\textrmSO_2n+1$ of purely bad parity}},
author = {Chi-Heng Lo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41742},
eprint = {2610.41742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41742},
}
RIS
TY - UNPB
TI - On unitary representations of p-adic Sp_2n and SO_2n+1 of purely bad parity
AU - Chi-Heng Lo
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41742
UR - https://arxiv.org/abs/2610.41742
AB - Let G be Sp_2n(F) or split SO_2n+1(F) over a non-archimedean local field F of characteristic zero. We classify the irreducible unitary representations of G of purely bad parity: such a representation is unitary if and only if it is of Arthur type, except for one additional family when G=Sp_2n(F). In particular, we confirm the remaining case of Ciubotaru's conjecture for SO_2n+1(F), namely that every unitary unipotent representation with integral infinitesimal parameter is of Arthur type.
ER -