Explicit computations in Hecke algebras of GL₂ over Dedekind domains

Ensenbach, Marc

doi:10.1090/S0002-9939-2013-11651-5

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

Proc. Amer. Math. Soc. 141 (2013), 3709-3722

DOI: https://doi.org/10.1090/S0002-9939-2013-11651-5

Published electronically: July 15, 2013

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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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