Dinakar Ramakrishnan
Published 2006-09-16, updated 2006-09-23Version 2
Irreducible representations are the building blocks of general, semisimple Galois representations \rho, and cuspidal representations are the building blocks of automorphic forms \pi of 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 \pi is implied by the irreducibility of \rho.
Comments: 36 pages; three references and a remark added in the replacement; to appear in "Representation Theory and Automorphic Forms", edited by T.Kobayashi, W.Schmid and J.H.Yang, Birkh\"auser
On parabolic induction on inner forms of the general linear group over a non-archimedean local field
Monodromy and irreducibility of type $A_1$ automorphic Galois representations
Stable automorphic forms for the general linear group
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