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Orbites unipotentes et poles d'ordre maximal de la fonction $μ$ de Harish-Chandra

Volker Heiermann
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Abstract

In a previous work, we have shown that a representation of a $p$-adic group obtained by (normalized) parabolic induction from an irreducible supercuspidal representation $σ$ of a Levi subgroup $M$ contains a subquotient which is square integrable, if and only if Harish-Chandra's $μ$-function has a pole in $σ$ of order equal to the parabolic rank of $M$. The aim of the present article is to interpret this result in terms of Langlands' functoriality principle.

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Volker Heiermann. 2004-04-07. Orbites unipotentes et poles d'ordre maximal de la fonction $μ$ de Harish-Chandra. https://arxiv.org/abs/math/0404177

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