U(g)-finite locally analytic representations
U(g)-finite locally analytic representations
复制标题
U(g)-有限局部解析表示
DOI：
10.1090/s1088-4165-01-00109-1
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
J. Teitelbaum
中科院分区：
文献类型：
--
作者：
P. Schneider;J. Teitelbaum
在本文中，我们继续研究的局部解析表示的$p$-adic李群$G$在向量空间上的一个球完备的非阿基米德域$K$，建立在代数方法，这样的表示介绍了我们的论文“局部解析分布和p-adic表示理论，与应用GL_2。“在那篇论文中，我们将G上局部解析分布的环D（G，K）上的模M与表示V相关联，并根据M的代数性质描述了V的容许条件。
本文确定了我们关于局部解析模的容许性条件与传统的Langlands理论的容许性之间的关系。然后，我们分析类的局部解析表示的属性，其相关的模块被湮没的理想的有限余维的通用包络代数G，显示在一些假设下，G，它们是总和的表示形式$X\otimes Y$，与X有限维和Y光滑。当X和Y是不可约的时，得到这种类型的不可约表示。
通过分析$SL_2（\Qp）$的局部解析主列的可约成员，我们得出结论。
In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations introduced in our paper "Locally analytic distributions and p-adic representation theory, with applications to GL_2." In that paper we associated to a representation $V$ a module $M$ over the ring $D(G,K)$ of locally analytic distributions on $G$ and described an admissibility condition on $V$ in terms of algebraic properties of $M$.
In this paper we determine the relationship between our admissibility condition on locally analytic modules and the traditional admissibility of Langlands theory. We then analyze the class of locally analytic representations with the property that their associated modules are annihilated by an ideal of finite codimension in the universal enveloping algebra of G, showing under some hypotheses on G that they are sums of representations of the form $X\otimes Y$, with X finite dimensional and Y smooth. The irreducible representations of this type are obtained when X and Y are irreducible.
We conclude by analyzing the reducible members of the locally analytic principal series of $SL_2(\Qp)$.