We establish an explicit Plancherel decomposition for \({{\,\mathrm{\mathrm {GL}}\,}}_n(F){\backslash } {{\,\mathrm{\mathrm {GL}}\,}}_n(E)\) where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai \(\gamma \)-factors. We also give two applications of this Plancherel formula: first to the global Ichino–Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by Zhang (J Am Math Soc 27:541–612, 2014) and secondly to the Hiraga–Ichino–Ikeda conjecture on formal degrees (J Am Math Soc 21(1):283–304, 2008) in the case of unitary groups.

我们为\（{{\，\ mathrm {\ mathrm {GL}} \，}} _ n（F）{\反斜杠} {{\，\ mathrm {\ mathrm {GL}} \，}建立显式Plancherel分解} _n（E）\），其中E / F是对Asai \（\ gamma \）因子使用局部函数方程的特征零局部场的二次扩展。我们还对该Plancherel公式进行了两个应用：首先，通过完成Zhang留下的局部相对字符之间的比较（J Am Math Soc 27：541–612，2014），对整体groups子的Ichino-Ikeda整体猜想；其次unit的情况下，Hiraga–Ichino–Ikeda猜想在形式度上（J Am Math Soc 21（1）：283–304，2008）。