Irreducibility and cuspidality
Dinakar Ramakrishnan
Abstract
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.
Create a lesson
Related papers
Value distribution of multiplicative functions along linear fractional sequences
Sun-Kai Leung
Delta theory of Anderson Modules II: Hodge-Pink structure
Sudip Pandit, Arnab Saha
Integers divisible by a shifted prime in a given interval
Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt et al.
On Piatetski-Shapiro primes from almost primes
Yuhua Zhao, Jinjiang Li, Linji Long et al.
On Consecutive Non-primitive Elements over Finite Fields
Bidushi Sharma, Dhiren Kumar Basnet
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu