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arXiv · 2201.12922

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

Gabriel Dospinescu·Vytautas Paškūnas·Benjamin Schraen
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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.

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Gabriel Dospinescu, Vytautas Paškūnas, Benjamin Schraen. 2022-01-30. Gelfand-Kirillov dimension and the $p$-adic Jacquet-Langlands correspondence. https://arxiv.org/abs/2201.12922

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