The Hecke-algebras related to the unimodular and modular group over the Hurwitz order of integral quaternions |
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Authors: | Aloys Krieg |
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Institution: | 1. Mathematisches Institut, Westf?lische Wilhelms-Universit?t, Einsteinstr. 62, D-4400, Münster, Federal Republic of Germany
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Abstract: | In the present paper the elementary divisor theory over the Hurwitz order of integral quaternions is applied in order to determine
the structure of the Hecke-algebras related to the attached unimodular and modular group of degreen. In the casen = 1 the Hecke-algebras fail to be commutative. Ifn > 1 the Hecke-algebras prove to be commutative and coincide with the tensor product of their primary components. Each primary
component turns out to be a polynomial ring inn resp.n + 1 resp. 2n resp. 2n+1 algebraically independent elements. In the case of the modular group of degreen, the law of interchange with the Siegel ϕ-operator is described. The induced homomorphism of the Hecke-algebras is surjective
except for the weightsr = 4n-4 andr = 4n-2. |
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Keywords: | Hecke-algebra unimodular group modular group quaternions Hurwitz order Siegel ϕ -operator |
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