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Standard Module Conjecture

V. Heiermann·G. Muic
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Abstract

Let G be a quasi-split p-adic group. Under the assumption that the local coefficients $C_ψ$ defined with respect to $ψ$-generic tempered representations of standard Levi subgroups of G are regular in the negative Weyl chamber, we show that the standard module conjecture is true, which means that the Langlands quotient of a standard module is generic if and only if the standard module is irreducible.

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V. Heiermann, G. Muic. 2006-03-16. Standard Module Conjecture. https://arxiv.org/abs/math/0603395

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