Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

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

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arXiv · 1408.0673

Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

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

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Abstract

Let $\mathcal{G}$ be a split reductive $p$-adic group with connected centre. We show that each Bernstein block in the principal series of $\mathcal{G}$ admits a definite geometric structure, namely that of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form $T//W$ where $T$ is a maximal torus in the Langlands dual group of $\mathcal{G}$ and $W$ is the Weyl group of $\mathcal{G}$.

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BibTeX RIS

Anne-Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld. 2014-08-04. Geometric structure for the principal series of a split reductive $p$-adic group with connected centre. https://arxiv.org/abs/1408.0673

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