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A Uniform Structure on Subgroups of GLn(Fq) and its Application to A Conditional Construction of Artin Representations of GLn
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Continuing our investigation in [19], where we associated an Artin representation to a vector-valued real analytic Siegel cusp form of weight (2, 1) under reasonable assumptions, we associate an Artin representation of GLn to a cuspidal representation of GLn(AQ) with similar assumptions. A main innovation in this paper is to obtain a uniform structure of subgroups in GLn(Fq ), which enables us to avoid complicated case by case analysis in [19]. We also supplement [19] by showing that we can associate non-holomorphic Siegel modular forms of weight (2, 1) to Maass forms for GL2(AQ) and to cuspidal representations of GL2(Ak ) where K is an imaginary quadratic field.
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