Simple Iwasawa modules with large canonical dimension of quaternion algebra over $\mathbb{Q}_p$
Representation Theory
2025-04-22 v1 Number Theory
Abstract
We construct certain absolutely irreducible Banach representations of the quaternion algebra of large canonical (Gelfand-Kirillov) dimension which yield counterexamples to a natural conjecture of Dospinescu-Schraen on the existence of an infinitesimal character and topological finite length for the locally analytic vectors of an absolutely irreducible Banach representation.
Keywords
Cite
@article{arxiv.2504.14490,
title = {Simple Iwasawa modules with large canonical dimension of quaternion algebra over $\mathbb{Q}_p$},
author = {Weibo Fu},
journal= {arXiv preprint arXiv:2504.14490},
year = {2025}
}
Comments
20 pages, comments welcome