Geodesic
Locally analytic distributions and 𝑝-adic representation theory, with applications to 𝐺𝐿₂
Schneider, Peter1 ; Teitelbaum, Jeremy2
1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
2 Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607
Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 443-468

Voir la notice de l'article provenant de la source American Mathematical Society

In this paper we study continuous representations of locally $L$-analytic groups $G$ in locally convex $K$-vector spaces, where $L$ is a finite extension of $\mathbb {Q}_p$ and $K$ is a spherically complete nonarchimedean extension field of $L$. The class of such representations includes both the smooth representations of Langlands theory and the finite dimensional algebraic representations of $G$, along with interesting new objects such as the action of $G$ on global sections of equivariant vector bundles on $p$-adic symmetric spaces. We introduce a restricted category of such representations that we call “strongly admissible” and we show that, when $G$ is compact, our category is anti-equivalent to a subcategory of the category of modules over the locally analytic distribution algebra of $G$. As an application we prove the topological irreducibility of generic members of the $p$-adic principal series for $GL_2(\mathbb {Q}_p)$. Our hope is that our definition of strongly admissible representation may be used as a foundation for a general theory of continuous $K$-valued representations of locally $L$-analytic groups.
DOI : 10.1090/S0894-0347-01-00377-0

Schneider, Peter 1 ; Teitelbaum, Jeremy 2

1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
2 Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607 
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Schneider, Peter; Teitelbaum, Jeremy. Locally analytic distributions and 𝑝-adic representation theory, with applications to 𝐺𝐿₂. Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 443-468. doi: 10.1090/S0894-0347-01-00377-0

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