A uniform structure on subgroups of GLn(double-struck Fq) and its application to a conditional construction of Artin representations of GLn

Henry H. Kim, Takuya Yamauchi

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Abstract

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(double-struck A) with similar assumptions. A main innovation in this paper is to obtain a uniform structure of subgroups in GLn(double-struck 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(double-struck A) and to cuspidal representations of GL2(double-struck AK) where K is an imaginary quadratic field.

Original languageEnglish
Pages (from-to)75-99
Number of pages25
JournalJournal of the Ramanujan Mathematical Society
Volume32
Issue number1
Publication statusPublished - 2017 Mar

ASJC Scopus subject areas

  • Mathematics(all)

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