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 |
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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♭. |
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ISSN: | 0001-8708 1090-2082 |
DOI: | 10.1016/j.aim.2023.108962 |