Haar Measure and the Artin Conductor

Author:

Gross Benedict,Gan Wee

Abstract

Let G G be a connected reductive group, defined over a local, non-archimedean field k k . The group G ( k ) G(k) is locally compact and unimodular. In On the motive of a reductive group, Invent. Math. 130 (1997), by B. H. Gross, a Haar measure | ω G | |\omega _G| was defined on G ( k ) G(k) , using the theory of Bruhat and Tits. In this note, we give another construction of the measure | ω G | |\omega _G| , using the Artin conductor of the motive M M of G G over k k . The equivalence of the two constructions is deduced from a result of G. Prasad.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

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4. Sign changes in harmonic analysis on reductive groups;Kottwitz, Robert E.;Trans. Amer. Math. Soc.,1983

5. Cambridge Studies in Advanced Mathematics;Laumon, Gérard,1996

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