Note on a conjecture of Braverman-Kazhdan

Given a connected reductive algebraic group G defined over a finite field Fq together with a representation ρ♭:G♭→GLN of the dual group of G (in the sense of Deligne-Lusztig), Braverman and Kazhdan [3] defined an exotic Fourier operator on the space of complex valued functions on G(Fq). Under some a...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2023-04, Vol.419, p.108962, Article 108962
Hauptverfasser: Laumon, Gérard, Letellier, Emmanuel
Format: Artikel
Sprache:eng
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Zusammenfassung:Given a connected reductive algebraic group G defined over a finite field Fq together with a representation ρ♭:G♭→GLN of the dual group of G (in the sense of Deligne-Lusztig), Braverman and Kazhdan [3] defined an exotic Fourier operator on the space of complex valued functions on G(Fq). Under some assumption on ρ♭, they gave a conjectural formula for the Fourier kernel which they prove when G=GLn for some n. In these notes we give a simple proof of their conjecture for any G without any assumption on ρ♭.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.108962