On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$

Santosh Nadimpalli; Mihir Sheth

doi:10.1016/j.jnt.2023.10.006

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arXiv · 2304.08218

On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$

Santosh Nadimpalli·Mihir Sheth

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Abstract

Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the integrality of generic irreducible locally algebraic representations. In this article, we prove the sufficiency of Emerton's conditions for some tamely ramified locally algebraic representations of $\mathrm{GL}_{2}(D)$ where $D$ is a $p$-adic division algebra.

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Santosh Nadimpalli, Mihir Sheth. 2024-10-09. On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$. https://doi.org/10.1016/j.jnt.2023.10.006

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