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Explicit computations in Hecke algebras of GL$ _2$ over Dedekind domains


Author: Marc Ensenbach
Journal: Proc. Amer. Math. Soc. 141 (2013), 3709-3722
MSC (2010): Primary 20G30, 20H05, 20C08
Published electronically: July 15, 2013
MathSciNet review: 3091763
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Abstract: In this paper, a formula for the number of right cosets contained in a double coset with respect to the unimodular group of invertible ( $ 2 \times 2$)-matrices over a Dedekind domain is developed. As applications we derive an index formula for congruence subgroups and an algorithm for the explicit calculation of products in Hecke algebras.


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Additional Information

Marc Ensenbach
Affiliation: Department of Mathematics, University of Siegen, 57068 Siegen, Germany
Email: ensenbach@mathematik.uni-siegen.de

DOI: https://doi.org/10.1090/S0002-9939-2013-11651-5
Keywords: Unimodular group, Dedekind domain, congruence subgroup, index formula, Hecke algebra
Received by editor(s): November 17, 2011
Received by editor(s) in revised form: January 11, 2012
Published electronically: July 15, 2013
Dedicated: Dedicated to the memory of Fritz Grunewald
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.