A Family of New-way Integrals for the Standard L-function of Cuspidal Representations of the Exceptional Group of Type G₂

2015/01/22 by Avner Segal, Segal, Avner
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1501.05558

openalex publication_date 2015/01/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let L^S(s,π,χ,\operatorname\mathfrakst) be a standard twisted partial L-function of degree 7 of the cuspidal automorphic representation π of the exceptional group of type G₂. In this paper we construct a family of Rankin-Selberg integrals representing this L-function. As an application, we prove that the representations attaining certain prescribed poles are exactly the representations attained by θ-lift from a group of finite type.

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