Number Theory Seminar

Let F be a function field and G a connected split reductive group over F. We define a "pseudo-identity operator" between spaces of automorphic functions on G(A)/G(F), and show that this operator is natural from the viewpoint of the geometric Langlands program via the functions-sheaves dictionary. We discuss how to define this operator over a number field by relating it to pseudo-Eisenstein series and inversion of the standard intertwining operator. The pseudo-identity operator is also connected to Deligne-Lusztig duality and cohomological duality of representations over a local field.