2023/12/04 by Hezi Halawi, Halawi, Hezi, Avner Segal +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2312.01686
openalex publication_date 2023/12/04 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
This manuscript has two goals: 1. To write an explicit description of the degenerate residual spectrum of the split, simple, simply-connected, exceptional groups of type En (for n=6,7,8). 2. To set a practical guide for similar calculations and, in particular, to describe various methods of ``computational representation theory'' relevant to the study of residues of automorphic Eisenstein series. In Part I we supply background information and notations from the theory of automorphic representations as well as concrete information on the exceptional groups of type En and their representation theory over non-Archimedean local fields. In Part II we make a systematic study of the residual spectrum of these groups where each chapter is devoted to a certain aspect of theory, it begins with methodical section and continues with sections devoted to the results for each of these groups. We describe completely the residual (square-integrable and non-square integrable) spectrum of the groups of type E6 and E7 and an almost complete description in the case of the group of type E8. We also study and list Siegel-Weil like identities between residual representations of these groups and list the Arthur parameters for their square-integrable residual representations.