Adelization of Automorphic Distributions and Mirabolic Eisenstein Series

TL;DR

This paper develops an adelic framework for automorphic representations of GL(n,R), analyzing automorphic distributions related to mirabolic Eisenstein series and deriving explicit functional equations involving intertwining operators.

Contribution

It introduces a new adelic approach to automorphic distributions for GL(n,R) and provides detailed analysis and explicit functional equations for mirabolic Eisenstein series.

Findings

Explicit functional equations for distributional pairings

Analysis of automorphic distributions for mirabolic Eisenstein series

Framework applicable to automorphic representations of GL(n,R)

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.