论文标题
抛物线寄生虫通过抛物线Pro-P $ iwahori-hecke代数
Parabolic Induction via the Parabolic pro-$p$ Iwahori--Hecke Algebra
论文作者
论文摘要
令$ \ mathbf {g} $为在本地紧凑的非Archimedean field $ f $上定义的连接的还原组，令$ \ mathbf {p} $是Levi $ \ Mathbf {M Mathbf {M} $的抛物线子群，并与Pro-P $ p $ p $ iwahori cubgrous complof of pro-p $ iwahori cubgrous a $ g：令$ r $为可交换的联合戒指。我们介绍了抛物线pro- $ p $ iwahorii-hecke $ r $ -Algebra $ \ Mathcal {h} _r（p）$ P：= \ Mathbf {p}（p}（p}（f）$，并构造两个$ r $ r $ r $ r $ -Algebra morphisms $θ^p_m the p_m \ colon \ colon \ colon \ colon \ Mathcalcal \ mathcal calcal cal____ \ Mathcal {h} _r（m）$和$ξ^p_g \ colon \ Mathcal \ Mathcal {h} _r（p）\ to \ Mathcal {h} _r（g）$ in Pro- $ p $ p $ p $ iwahori-hecke $ iwahori-hecke $ r $ r $ r $ - algebra of $ m：m：= $ = $ = $ = \ g $}我们证明了结果函数mod-$ \ nathcal {h} _r（m）\ to $ mod- $ \ $ \ mathcal {h} _r（g）$来自右$ \ nathcal {h} _r（h} _r（m）$ - modules $ prut $ \ nathcal ost $ mod的类别， $θ^p_m $和沿$ξ^p_g $的标量扩展与由于ollivier-vignéras而引起的抛物线诱导。通过通用的subalgebra $ \ Mathcal {h} _r（m，g）$ of $ \ MATHCAL {h} _r（g）$，与$ \ Mathcal {h} _r（g）$，与$ \ MATHCAL {h} $非常相似，MAPS $θ^p_m $和$ξ^p_g $ factor the MAPS $θ^p_g $。研究这些代数$ \ MATHCAL {h} _r（m，g）$ for Varying $（m，g）$，我们证明了张量产品的过渡性属性。作为应用程序，我们给出了抛物线诱导的传递性的新证明。
Let $\mathbf{G}$ be a connected reductive group defined over a locally compact non-archimedean field $F$, let $\mathbf{P}$ be a parabolic subgroup with Levi $\mathbf{M}$ and compatible with a pro-$p$ Iwahori subgroup of $G := \mathbf{G}(F)$. Let $R$ be a commutative unital ring. We introduce the parabolic pro-$p$ Iwahori--Hecke $R$-algebra $\mathcal{H}_R(P)$ of $P := \mathbf{P}(F)$ and construct two $R$-algebra morphisms $Θ^P_M\colon \mathcal{H}_R(P)\to \mathcal{H}_R(M)$ and $Ξ^P_G\colon \mathcal{H}_R(P) \to \mathcal{H}_R(G)$ into the pro-$p$ Iwahori--Hecke $R$-algebra of $M := \mathbf{M}(F)$ and $G$, respectively. We prove that the resulting functor Mod-$\mathcal{H}_R(M) \to$ Mod-$\mathcal{H}_R(G)$ from the category of right $\mathcal{H}_R(M)$-modules to the category of right $\mathcal{H}_R(G)$-modules (obtained by pulling back via $Θ^P_M$ and extension of scalars along $Ξ^P_G$) coincides with the parabolic induction due to Ollivier--Vignéras. The maps $Θ^P_M$ and $Ξ^P_G$ factor through a common subalgebra $\mathcal{H}_R(M,G)$ of $\mathcal{H}_R(G)$ which is very similar to $\mathcal{H}_R(M)$. Studying these algebras $\mathcal{H}_R(M,G)$ for varying $(M,G)$ we prove a transitivity property for tensor products. As an application we give a new proof of the transitivity of parabolic induction.
