Simple Iwasawa modules with large canonical dimension of quaternion algebra over ℚ_p

2025/04/20 by Fu, Weibo
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.14490

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.

Related

• On the finite length of some p-adic representations of the quaternion algebra over \Q_p
• On some p-adic and mod p representations of quaternion algebra over ℚ_p
• Gelfand-Kirillov dimension and the p-adic Jacquet-Langlands correspondence
• On some mod p representations of quaternion algebra over ℚ_p
• The canonical dimension of modules for Iwasawa algebras