Rationality for isobaric automorphic representations: the CM-case

Introduction to Automorphic Representations

Unipotent Automorphic Representations : Conjectures

In these notes, we shall attempt to make sense of the notions of semisimple and unipotent representations in the context of automorphic forms. Our goal is to formulate some conjectures, both local and global, which were originally motivated by the trace formula. Some of these conjectures were stated less generally in lectures [2] at the University of Maryland. The present paper is an update of ...

A Descent Criterion for Isobaric Representations

This will appear as an appendix to the paper Functoriality for the exterior square of GL4 and the symmetric fourth of GL2 ([K]) by Henry Kim. The object here is to prove the following extension (from cuspidal) to isobaric automorphic representations of Proposition 3.6.1 of [Ra], which was itself an extension to GL(n) of the Proposition 4.2 (for GL(2)) in [BR]. The argument is essentially the sa...

On Strong Multiplicity One for Automorphic Representations

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

Automorphic Representations of Adele Groups