Irreducibility and Cuspidality

Abstract

Suppose ρ is an n-dimensional representation of the absolute Galois group of Q which is associated, via an identity of L-functions, with an automorphic representation π of GL(n) of the adele ring of Q. It is expected that π is cuspidal if and only if ρ is irreducible, though nothing much is known in either direction in dimensions > 2. The object of this article is to show for n < 6 that the cuspidality of a regular algebraic π is implied by the irreducibility of ρ. For n < 5, it suffices to assume that π is semi-regular.

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