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arXiv · 1307.2605

Twisting of paramodular vectors

Jennifer Johnson-Leung·Brooks Roberts
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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.

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Jennifer Johnson-Leung, Brooks Roberts. 2013-07-09. Twisting of paramodular vectors. https://arxiv.org/abs/1307.2605

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