• The Hecke-algebras related to the unimodular and modular group over the Hurwitz order of integral quaternions

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      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0201-0229

    • Keywords

       

      Hecke-algebra; unimodular group; modular group; quaternions; Hurwitz order; Siegel ϕ-operator

    • 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.

    • Author Affiliations

       

      Aloys Krieg1

      1. Mathematisches Institut, Westfälische Wilhelms-Universität, Einsteinstr. 62, Münster - D-4400, Federal Republic of Germany
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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