A theory of γ-factors for G₂ × GL_r

2023/08/24 by Wee Teck Gan, Gan, Wee Teck, Gordan Savin +1
Mathematics · #11F70 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2308.12561

openalex publication_date 2023/08/24 · openalex created_date 2023/08/26 · openalex updated_date 2026/07/28

Abstract

We construct a theory of local gamma factors for G₂ × GL_r using a functorial lifting from G₂ to GL₇. This theory of gamma factors is uniquely characterized by a usual list of properties, showing that it is the only possible candidate. Moreover, this theory of gamma factors is compatible with the Galois theoretic one under the local Langlands correspondence for G₂.

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