Abstract
Let F be a nonarchimedean local field of characteristic zero. In this chapter we prove a number of important results concerning stable Klingen vectors in representations of GSp(4,F)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathrm {GSp}(4,F)$$\end{document} induced from the Siegel parabolic subgroup P of GSp(4,F)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathrm {GSp}(4,F)$$\end{document}. These results are key ingredients for the dimension formulas proved in the next chapter.