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arXiv · 2209.05536

On irreps of a Hecke algebra of a non-reductive group

David Kazhdan·Alexander Yom Din
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Abstract

We study irreducible representations of the Hecke algebra of the pair $({\rm PGL}_2 (F[ε] / (ε^2)) , {\rm PGL}_2 (\mathcal{O}[ε] / (ε^2)))$ where $F$ is a local non-Archimedean field of characteristic different than $2$ and $\mathcal{O} \subset F$ is its ring of integers. We expect to apply our analysis to the study of the spectrum of Hecke operators on the space of cuspidal functions on the space of principal ${\rm PGL}_2$-bundles on curves over rings $\mathbb{F}_q [ε] / (ε^2)$.

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David Kazhdan, Alexander Yom Din. 2022-09-12. On irreps of a Hecke algebra of a non-reductive group. https://arxiv.org/abs/2209.05536

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