Resolutions of locally analytic principal series representations of $GL_2$

Aranya Lahiri

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arXiv · 2008.04503

Resolutions of locally analytic principal series representations of $GL_2$

Aranya Lahiri

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Abstract

For a finite field extension $F/\mathbb{Q}_p$ we associate a coefficient system attached on the Bruhat-Tits tree of $G:= {\rm GL}_2(F)$ to a locally analytic representation $V$ of $G$. This is done in analogy to the work of Schneider and Stuhler for smooth representations. This coefficient system furnishes a chain-complex which is shown, in the case of locally analytic principal series representations $V$, to be a resolution of $V$.

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Aranya Lahiri. 2020-08-11. Resolutions of locally analytic principal series representations of $GL_2$. https://arxiv.org/abs/2008.04503

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