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arXiv · 2606.14485

A nonabelian Fourier transform for tempered unipotent representations, II

Anne-Marie Aubert·Dan Ciubotaru·Beth Romano
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Abstract

We extend the construction of the nonabelian Fourier transform proposed in our previous paper from the space of unipotent elliptic characters to the space of unipotent compact characters of a reductive $p$-adic group, and we investigate its relation with the branching to maximal compact open subgroups. We prove that this Fourier transform is compatible with parahoric restriction for certain groups, including $\mathrm{SL}_n, \mathrm{GL}_n$, and $G_2$. We also relate the compact setting to the elliptic setting using parabolic induction.

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Anne-Marie Aubert, Dan Ciubotaru, Beth Romano. 2026-06-12. A nonabelian Fourier transform for tempered unipotent representations, II. https://arxiv.org/abs/2606.14485

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