Abstract
The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms. Let X be a curve over Fq, F its function field and A the adele ring of F. In this paper we will exhibit the first properties for the graph of Hecke operators for GLn(A), for every n≥1. This includes a description of the graph in terms of coherent sheaves on X. We provide a numerical condition for two vertices to be connected by an edge. Moreover, we describe how to calculate these graphs in the case of the projective line X=P1(Fq).
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