Gelfand-Kirillov dimension and the p-adic Jacquet-Langlands correspondence

2022/01/30 by Dospinescu, Gabriel, Paškūnas, Vytautas, Schraen, Benjamin · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.12922

Abstract

We bound the Gelfand-Kirillov dimension of unitary Banach space representations of p-adic reductive groups, whose locally analytic vectors afford an infinitesimal character. We use the bound to study Hecke eigenspaces in completed cohomology of Shimura curves and p-adic Banach space representations of the group of units of a quarternion algebra over \mathbb Q_p appearing in the p-adic Jacquet-Langlands correspondence, deducing finiteness results in favourable cases.

Cited by

• On the finite length of some p-adic representations of the quaternion algebra over \Q_p

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