论文标题
函数$ \ check {\ mathcal {f}}^g_p $在$ k_0 $的级别
The functor $\check{\mathcal{F}}^G_P$ at the level of $K_0$
论文作者
论文摘要
令$ g $为$ p $ - adic lie Group，带有还原的lie代数$ \ mathfrak {g} $。用$ d（g）$表示本地分析分布代数为$ g $。 Orlik-trauch和Agrawal-Strauch研究了在$ \ Mathfrak {G} $的各个类别上定义的某些确切函数 - 在本地分析$ G $ -Presentations或$ d（g）$ - 模块的类别中具有图像的表示。在本文中，我们证明，对于$ d（g）$ - 模块的适当定义类别，该函子在Grothendieck组的水平上产生了注射式同构。我们还解释了该函子如何在Grothendieck组级别与翻译函数相互作用。
Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. Denote by $D(G)$ the locally analytic distribution algebra of $G$. Orlik-Strauch and Agrawal-Strauch have studied certain exact functors defined on various categories of $\mathfrak{g}$-representations with image in the category of locally analytic $G$-representations or $D(G)$-modules. In this paper we prove that for suitably defined categories of $D(G)$-modules, this functor gives rise to injective homomorphisms at the level of Grothendieck groups. We also explain how this functor interacts with translation functors at the level of Grothendieck groups.
