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arXiv · 2608.21981

Admissibility of Bernstein centers

Tsao-Hsien Chen·Cheng-Chiang Tsai
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Abstract

We provide a criterion for determining when elements of the Bernstein center of a totally disconnected locally compact group are admissible invariant distributions in the sense of Harish-Chandra \cite{HC99}. As a consequence, we deduce the local integrability results for elements of bounded depth or Bernstein supports in the Bernstein centers of reductive $p$-adic groups. Our methods apply uniformly to both complex and mod-$\ell$ coefficients, generalizing results of Moy and Tadić \cite{MT02} in the complex case.

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Tsao-Hsien Chen, Cheng-Chiang Tsai. 2026-08-22. Admissibility of Bernstein centers. https://arxiv.org/abs/2608.21981

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