Adelization of Automorphic Distributions and Mirabolic Eisenstein Series
Number Theory
2011-06-15 v1 Representation Theory
Abstract
Automorphic representations can be studied in terms of the embeddings of abstract models of representations into spaces of functions on Lie groups that are invariant under discrete subgroups. In this paper we describe an adelic framework to describe them for the group GL(n,R), and provide a detailed analysis of the automorphic distributions associated to the mirabolic Eisenstein series. We give an explicit functional equation for some distributional pairings involving this mirabolic Eisenstein distribution, and the action of intertwining operators.
Keywords
Cite
@article{arxiv.1106.2583,
title = {Adelization of Automorphic Distributions and Mirabolic Eisenstein Series},
author = {Stephen D. Miller and Wilfried Schmid},
journal= {arXiv preprint arXiv:1106.2583},
year = {2011}
}
Comments
46 pages, to appear in Contemporary Mathematics, volume in honor of Gregg Zuckerman's 60th birthday edited by Jeff Adams, Bong Lian and Siddhartha Sahi