Twisting of paramodular vectors

Abstract

Let $F$ be a non-archimedean local field of characteristic zero, let $(\pi ,V)$ be an irreducible, admissible representation of $\GSp(4,F)$ with trivial central character, and let $\chi$ be a quadratic character of $F^{\times }$ with conductor $c(\chi )>1$. We define a twisting operator $T_{\chi }$ from paramodular vectors for $\pi$ of level $n$ to paramodular vectors for $\chi \otimes \pi$ of level $\max (n+2c(\chi ),4c(\chi ))$, and prove that this operator has properties analogous to the well-known $\GL(2)$ twisting operator.