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arXiv · 2410.10761

On the Braverman-Kazhdan-Ngo Triples

Dihua Jiang·Zhaolin Li·Guodong Xi
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Abstract

In the Braverman-Kazhdan proposal and certain refinement of Ngo for automorphic $L$-functions, the reductive group $G$ and the representations $\rho$ of the Langlands dual group $G^\vee$ are taken with certain assumptions. We introduce the notion of the Braverman-Kazhdan-Ngo triples $(G,G^\vee,\rho)$ 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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Dihua Jiang, Zhaolin Li, Guodong Xi. 2024-10-14. On the Braverman-Kazhdan-Ngo Triples. https://doi.org/10.2140/pjm.2026.340.309

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