The exterior square L-function on GU(2,2)

2015/05/10 by Aaron Pollack, Pollack, Aaron
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1505.02337

openalex publication_date 2015/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give Rankin-Selberg integrals for the quasisplit unitary group on four variables, GU(2,2), and a closely-related quasisplit form of GSpin₆. First, we give a two-variable Rankin-Selberg integral on GU(2,2). This integral applies to generic cusp forms, and represents the product of the exterior square (degree six) L-function and the standard (degree eight) L-function. Then we give a set of integral representations for just the degree six L-function on the quasisplit GSpin₆. The GSpin₆ integrals are reinterpretations of an integral originally considered by Gritsenko for Hermitian modular forms. We show that they unfold to a model that is not unique, and analyze the integrals via the technique of Piatetski-Shapiro and Rallis.

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