On the Braverman-Kazhdan-Ngo Triples

2024/10/14 by Jiang, Dihua, Li, Zhaolin, Xi, Guodong
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.10761

Abstract

In the Braverman-Kazhdan proposal and certain refinement of Ngo for automorphic L-functions, the reductive group G and the representations ρ of the Langlands dual group G^\vee are taken with certain assumptions. We introduce the notion of the Braverman-Kazhdan-Ngo triples (G,G^\vee,ρ) and show that for general automorphic L-functions, it is enough to consider the Braverman-Kazhdan-Ngo triples. We also verify that for a given Braverman-Kazhdan-Ngo triple, the reductive monoid constructed from the Vinberg method and that constructed from the Putcha-Renner method are isomorphic.

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