Irreducibility criteria for local and global representations

Narita, Hiro-aki; Pitale, Ameya; Schmidt, Ralf

doi:10.1090/S0002-9939-2012-11438-8

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Irreducibility criteria for local and global representations

Authors: Hiro-aki Narita, Ameya Pitale and Ralf Schmidt
Journal: Proc. Amer. Math. Soc. 141 (2013), 55-63
MSC (2010): Primary 11F46, 11F50, 11F70; Secondary 22E50, 22E55
Posted: May 1, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that certain types of modular cusp forms generate irreducible automorphic representations of the underlying algebraic group. Analogous Archimedean and non-Archimedean local statements are also given.

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Additional Information

Hiro-aki Narita
Affiliation: Department of Mathematics, Kumamoto University, Kurokami, Kumamoto 860-8555, Japan
Email: narita@sci.kumamoto-u.ac.jp

Ameya Pitale
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: apitale@math.ou.edu

Ralf Schmidt
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: rschmidt@math.ou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11438-8
PII: S 0002-9939(2012)11438-8
Keywords: Representation over local fields, automorphic representation, Hecke eigenvector
Received by editor(s): June 6, 2011
Posted: May 1, 2012
Additional Notes: The first author was partly supported by Grant-in-Aid for Young Scientists (B) 21740025, the Ministry of Education, Culture, Sports, Science and Technology, Japan
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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