论文标题
Gelfand-Graev代表的主要系列组成部分
Principal series component of Gelfand-Graev representation
论文作者
论文摘要
让$ g $为在非Archimedean本地字段$ f $上定义的连接还原组。让$ b $为Levi Factor $ t $和Uniptent Radical $ U $的最小$ f $ f $ - parabolic子组。令$ψ$为$ u（f）$和$λ$的非脱位字符，$ t（f）$。令$（k，ρ）$是与$ g（f）$的伯恩斯坦块相关的bushnell-kutzko类型，由$（t，λ）$确定。我们研究$ρ$ - 异型组件$（c \ text {-ind} _ {u（f）}^{g（f）}^{g（f）}ψ）^ρ$的诱导空间$ c \ c \ text {-ind} _ {u（f）我们表明$（c \ text {-ind} _ {u（f）}^{g（f）ψ）^ρ$是Hecke algebra $ \ Mathcal {h}（h}（g，ρ）$（k，k，ρ）$相关的Hecke Algebra $ \ MathCal {h}（g，ρ）$。当$ t $拆分时，我们会以$ \ Mathcal {h}（g，ρ）$更明确地描述它。我们对$ f $的残留特性做出了假设，后来又对$ f $的特征和$ g $的中心做出了假设，具体取决于$ $（t，λ）$。我们的结果将Chan和Savin的主要结果推广到\ cite {cs18}中，后者对$ t $ split的$λ= 1 $进行了处理。
Let $G$ be a connected reductive group defined over a non-archimedean local field $F$. Let $B$ be a minimal $F$-parabolic subgroup with Levi factor $T$ and unipotent radical $U$. Let $ψ$ be a non-degenerate character of $U(F)$ and $λ$ a character of $T(F)$. Let $(K,ρ)$ be a Bushnell-Kutzko type associated to the Bernstein block of $G(F)$ determined by the pair $(T,λ)$. We study the $ρ$-isotypical component $(c\text{-ind}_{U(F)}^{G(F)}ψ)^ρ$ of the induced space $c\text{-ind}_{U(F)}^{G(F)}ψ$ of functions compactly supported mod $U(F)$. We show that $(c\text{-ind}_{U(F)}^{G(F)}ψ)^ρ$ is cyclic module for the Hecke algebra $\mathcal{H}(G,ρ)$ associated to the pair $(K,ρ)$. When $T$ is split, we describe it more explicitly in terms of $\mathcal{H}(G,ρ)$. We make assumptions on the residue characteristic of $F$ and later also on the characteristic of $F$ and the center of $G$ depending on the pair $(T,λ)$. Our results generalize the main result of Chan and Savin in \cite{CS18} who treated the case of $λ=1$ for $T$ split.
