Dimensions of some locally analytic representations

Schmidt, Tobias; Strauch, Matthias

doi:10.1090/ert/475

Dimensions of some locally analytic representations
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by Tobias Schmidt and Matthias Strauch

Represent. Theory 20 (2016), 14-38

DOI: https://doi.org/10.1090/ert/475

Published electronically: February 2, 2016

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Abstract:

Let $G$ be the group of points of a split reductive group over a finite extension of $\mathbb {Q}_p$. In this paper, we compute the dimensions of certain classes of locally analytic $G$-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on $p$-adic symmetric spaces. As an application, we compute the dimensions of the unitary $\textrm {GL}_2(\mathbb {Q}_p)$-representations appearing in Colmez’ $p$-adic local Langlands correspondence.

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