Twisting of paramodular vectors

Original · EN

Let F be a non-archimedean local field of characteristic zero, let (π,V) be an irreducible, admissible representation of (4,F) with trivial central character, and let χ be a quadratic character of F× with conductor c(χ)>1. We define a twisting operator Tχ from paramodular vectors for π of level n to paramodular vectors for χ⊗ π of level (n+2c(χ),4c(χ)), and prove that this operator has properties analogous to the well-known (2) twisting operator.