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arXiv · 1512.08637

Bernstein components via Bernstein center

Alexander Braverman·David Kazhdan·Roman Bezrukavnikov
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Abstract

Let G be a reductive p-adic group. Let $Φ$ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that $Φ$ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr(G); in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modiification of the arguments of J.F.Dat who proved our result in one direction.

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Alexander Braverman, David Kazhdan, Roman Bezrukavnikov. 2018-10-12. Bernstein components via Bernstein center. https://arxiv.org/abs/1512.08637

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