A uniform structure on subgroups of GL(n)(F-q) and its application to a conditional construction of Artin representations of GL(n)

作者：Kim Henry H^*; Yamauchi Takuya

来源：Journal of the Ramanujan Mathematical Society, 2017, 32(1): 75-99.

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 GL(n) to a cuspidal representation of GLn(A(Q)) with similar assumptions. A main innovation in this paper is to obtain a uniform structure of subgroups in GLn(F-q), 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 GL(2)(A(Q)) and to cuspidal representations of GL2(A(K)) where K is an imaginary quadratic field.

• 出版日期2017-3