Constructions of global integrals in the exceptional groups

2011/08/05 by David Ginzburg, Joseph Hundley, Ginzburg, David +1
Mathematics · #32N10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1108.1401

openalex publication_date 2011/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by known examples of global integrals which represent automorphic L-functions, this paper initiates the study of a certain two-dimensional array of global integrals attached to any reductive algebraic group, indexed by maximal parabolic subgroups in one direction and by unipotent conjugacy classes in the other. Fourier coefficients attached to unipotent classes, Gelfand-Kirillov dimension of automorphic representations, and an identity which, empirically, appears to constrain the unfolding process are presented in detail with examples selected from the exceptional groups. Two new Eulerian integrals are included among these examples.

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