Hecke algebras related to the unimodular and modular groups over quadratic field extensions and quaternion algebras
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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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1321-1331
- MSC (2010): Primary 11F60
- DOI: https://doi.org/10.1090/S0002-9939-2010-10570-1
- MathSciNet review: 2748425