The principal series of $p$-adic groups with disconnected centre

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

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arXiv · 1409.8110

The principal series of $p$-adic groups with disconnected centre

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

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Abstract

Let G be a split connected reductive group over a local non-archimedean field. We classify all irreducible complex G-representations in the principal series, irrespective of the (dis)connectedness of the centre of G. This leads to a local Langlands correspondence for principal series representations, which satisfies all expected properties. We also prove that the ABPS conjecture about the geometric structure of Bernstein components is valid throughout the principal series of G.

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Anne-Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld. 2014-09-29. The principal series of $p$-adic groups with disconnected centre. https://arxiv.org/abs/1409.8110

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