# 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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