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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hecke algebras related to the unimodular and modular groups over quadratic field extensions and quaternion algebras


Author: Martin Raum
Journal: Proc. Amer. Math. Soc. 139 (2011), 1321-1331
MSC (2010): Primary 11F60
Published electronically: September 3, 2010
MathSciNet review: 2748425
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Abstract: We investigate the structure of the Hecke algebras related to the unimodular and modular groups over quadratic field extensions and quaternion algebras. In particular, we show that in general there is no decomposition into primary components. We give a set of generators, and in some special cases we deduce the commutation relation with the Siegel $ \Phi$-operator.


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Additional Information

Martin Raum
Affiliation: Lehrstuhl A für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
Address at time of publication: MPI für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Email: Martin.Raum@matha.rwth-aachen.de, mraum@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10570-1
PII: S 0002-9939(2010)10570-1
Received by editor(s): December 22, 2009
Received by editor(s) in revised form: April 27, 2010, and May 2, 2010
Published electronically: September 3, 2010
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.