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Journal of the Ramanujan Mathematical Society

Volume 32, Issue 1, March 2017  pp. 75–99.

A uniform structure on subgroups of GL n(Fq) and its application to a conditional construction of Artin representations of GLn

Authors:  Henry H. Kim and Takuya Yamauchi
Author institution:Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada and Korea Institute for Advanced Study, Seoul, Korea

Summary:  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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