Year: 2026
Type: preprint
Abstract: Let $p$ be an odd prime and $f \geq 1$. We consider a $p$-adic locally algebraic $\text{GL}_2(\mathbb Q_{p^f})$-representation attached to a tuple of $f$ weights $k=(k_i)$ for $0 \leq i \leq f-1$ and a $p$-adic integer $a_p$ with valuation in $(0,1)$. We give conditions under which the irreducible quotients of the subquotients in a filtration on the reduction mod $p$ of the natural integral structure on this space are supercuspidal. We also check that for small $k$ and $f$ the integral structure is a lattice so that the mod $p$ reduction is nonzero.
Source: arXiv (Cornell University)
Authors: Ghate, Eknath, Pandey, Shivansh
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160316899