On some $p$-adic and mod $p$ representations of quaternion algebra over ${\mathbb{Q}}_p$

Abstract

Let $D$ be the non-split quaternion algebra over ${\mathbb{Q}}_p$. We prove that a class of admissible unitary Banach space representations of $D^{\times }$ of global origin are topologically of finite length.

38 pages. Comments welcome !

Cited by in corpus (1)

• Restriction of $p$-adic representations of ${\mathrm{GL}}_2({\mathbf{Q}}_p)$ to parahoric subgroups