arXiv subjects

Reinier Sorgdrager

Publications and source records attributed to Reinier Sorgdrager.

2 recordsLinked to original sources

arXiv2026

Gelfand-Kirillov bound for $p$-adic Banach representations with infinitesimal character for $\text{GL}_2$ and quaternion units

We prove that an admissible $p$-adic Banach representation of $\text{GL}_2K$ whose locally analytic vectors have an infinitesimal character has Gelfand-Kirillov dimension $\leq[K\colon\mathbf Q_p]$, where $p>2$ and $K$ is a $p$-adic field. We also prove this for the group of units of the quaternions over $K$ replacing $\text{GL}_2K$. In the process, we make some observations in the theory of $p$-adic Banach representations that might be of independent interest.

math.RT↗

arXiv2025

Note on a certain category of mod $p$ representations

Let $p>3$ be a prime number, $f\geq1$ an integer. We consider a certain full subcategory $\mathcal C$ of the category of smooth admissible mod $p$ representations of either $\text{GL}_2\mathbf Q_{p^f}$ or of the group of units of the quaternion algebra over $\mathbf Q_{p^f}$. This category was introduced in the context of the mod $p$ Langlands program by Breuil-Herzig-Hu-Morra-Schraen in the $\text{GL}_2$-case and by Hu-Wang in the quaternion case. We prove that whether a smooth admissible mod $p$ representation $\pi$ (with central character) belongs to $\mathcal C$ is completely determined by the restriction of $\pi$ to an arbitrarily small open subgroup.

math.RT↗