2006/09/16 by Dinakar Ramakrishnan, Ramakrishnan, Dinakar
Mathematics · #11F70 #11F80 #22E55 #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.math/0609460
openalex publication_date 2006/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Irreducible representations are the building blocks of general, semisimple Galois representations ρ, and cuspidal representations are the building blocks of automorphic forms πof the general linear group. It is expected that when an object of the former type is associated to one of the latter type, usually in terms of an identity of L-functions, the irreducibility of the former should imply the cuspidality of the latter, and vice-versa. It is not a simple matter - at all - to prove this expectation in either direction, and nothing much is known in dimensions >2. The main result of this article shows for n < 6, in particular, that the cuspidality of a regular algebraic πis implied by the irreducibility of ρ.