论文标题
广义惠特克功能和雅克模块
Generalized Whittaker functions and Jacquet modules
论文作者
论文摘要
令$ g $为非阿基梅德本地字段的还原组，而$ψ$是最小抛物线子群的一级激进$ u_0 $的非脱位特征，$ p_0 = m_0u_0 $。对于$ p = mu \ supseteq p_0 $，我们证明了delorme的常数term映射的jacquet模块$ j_p（\ mathcal {w}（w}（g，ψ））$从space $ \ mathcal {w}（w}（g，ψ）$ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ $ \ MATHCAL {W}（M，ψ_{| U_0 \ CAP M}）$是Bushnell和Henniart的倒数的双映射，来自$ J_ {p^ - }（\ Mathcal {w} $ \ MATHCAL {W} _C（M，ψ_{| U_0 \ CAP M}^{ - 1}）$（特别是常数术语映射是汇总的）。我们提供了此结果的应用。我们还提供了Lapid和Mao在$ \ ell $ -ADIC表示的上下文中的整体广义Whittaker功能的渐近扩展的整体版本。
Let $G$ be a reductive group over a non archimedean local field, and $ψ$ a non-degenerate character of the unipotent radical $U_0$ of a minimal parabolic subgroup $P_0=M_0U_0$. For $P=MU\supseteq P_0$, we show that the descent to the Jacquet module $J_P(\mathcal{W}(G,ψ))$ of Delorme's constant term map from the space $\mathcal{W}(G,ψ)$ of generalized Whittaker functions on $G$ to $\mathcal{W}(M,ψ_{|U_0\cap M})$ is the dual map of the inverse of the isomorphism of Bushnell and Henniart from $J_{P^-}(\mathcal{W}_c(G,ψ^{-1}))$ to $\mathcal{W}_c(M,ψ_{|U_0\cap M}^{-1})$ (in particular the constant term map is surjective). We give applications of this result. We also provide an integral version of Lapid and Mao's asymptotic expansion for integral generalized Whittaker functions in the context of $\ell$-adic representations.
