Smooth Duals of Inner Forms of $GL_n$ and $SL_n$

Anne-Marie Aubert; Paul Baum; Roger Plymen; Maarten Solleveld

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arXiv · 1505.04361

Smooth Duals of Inner Forms of $GL_n$ and $SL_n$

Anne-Marie Aubert·Paul Baum·Roger Plymen·Maarten Solleveld

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Abstract

Let $F$ be a non-archimedean local field. We prove that every Bernstein component in the smooth dual of each inner form of the general linear group $GL_n(F)$ is canonically in bijection with the extended quotient for the action, given by Bernstein, of a finite group on a complex torus. For inner forms of $SL_n(F)$ we prove that each Bernstein component is canonically in bijection with the associated twisted extended quotient. In both cases, the bijections satisfy naturality properties with respect to the tempered dual, parabolic induction, central character, and the local Langlands correspondence.

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BibTeX RIS

Anne-Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld. 2015-05-17. Smooth Duals of Inner Forms of $GL_n$ and $SL_n$. https://arxiv.org/abs/1505.04361

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