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Irreducibility and Cuspidality

Ramakrishnan, Dinakar (2007) Irreducibility and Cuspidality. In: Representation theory and automorphic forms. Progress in Mathematics. No.255. Birkhäuser , Boston, pp. 1-27. ISBN 978-0-8176-4505-2.

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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.

Item Type:Book Section
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Additional Information:© 2008 Birkhäuser Boston. Partially supported by the NSF through the grant DMS-0402044.
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Subject Keywords:irreducibility; Galois representations; cuspidality; automorphic representations; general linear group; symplectic group; regular algebraic representations
Series Name:Progress in Mathematics
Issue or Number:255
Classification Code:Subject Classifications: 11F70; 11F80; 22E55
Record Number:CaltechAUTHORS:20100721-134623343
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19145
Deposited By: Tony Diaz
Deposited On:30 Jul 2010 21:47
Last Modified:08 Nov 2021 23:50

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