关于逆表示的可微向量

Types et contragrédientes

Let G be a p-adic reductive group, and R an algebraically closed field. Let us consider a smooth representation of G on an R-vector space V. Fix an open compact subgroup K of G and a smooth irreducible representation of K on a finite-dimensional R-vector space W. The space of K-homomorphisms from W to V is a right module over the intertwining algebra H(G,K,W). We examine how those constructions behave when we pass to the contragredient representations of V and W, and we give conditions under which the behaviour is the same as in the case of complex representations. We take an abstract viewpoin…

关于Infinite Dimensional李群表示的可微向量

On Differentiable Vectors for Representations of Infinite Dimensional Lie Groups

在本文中，我们开发了两种类型的工具来处理的连续表示$π\: G \to \GL(V)$的无限维李群$G$局部凸空间$V$上的向量的可微性。第一类结果涉及光滑向量空间$V^\infty$。如果$G$是一个Banach-李群，我们定义一个拓扑空间$V^\infty$上的光滑向量的$G$在这个空间上的作用是光滑的。如果$V$是Banach空间，则$V^\infty$是Fréchet空间。这特别适用于$C^*$ -动力系统$(\cA,G, α)$，其中$G$是一个Banach-李群。对于酉表示，我们证明了一个向量$v$是光滑的，如果相应的正定函数$\la π(g)v,v\ra$是光滑的。第二类结果涉及标准的$C^k$ -向量的运营商的派生代表的Banach-李群$G$作用于Banach空间$V$。特别是，我们为每个$k \in \N$提供连续酉表示的例子，其中$C^{k+1}$ -向量的空间是平凡的，并且$C^k$ -向量的空间是稠密的。

Frechet-Lie超群的可微向量与酉表示

Differentiable vectors and unitary representations of Frechet-Lie supergroups

对于具有Trotter性质的局部凸李群，证明了酉表示的k次可微向量空间等于李代数作用的k重积整环的交.这个结果也适用于可度量化局部凸空间上局部指数群的连续表示。作为应用，我们将李超群表示论中的一个关键稳定性定理扩展到Banach情形之外。

向量在李群表示中的可微性

On differentiability of vectors in Lie group representations

本文讨论了局部凸空间上无限维李群表示中可微向量的线性问题，它类似于函数的方向导数的线性问题.

Deformations of vector bundles in the categories of Lie algebroids and groupoids

This thesis deals with deformations of VB-algebroids and VB-groupoids. They can be considered as vector bundles in the categories of Lie algebroids and groupoids and encompass several classical objects, including Lie algebra and Lie group representations, 2-vector spaces and the tangent and the cotangent algebroid (groupoid) to a Lie algebroid (groupoid). Moreover, they are geometric models for some kind of representations of Lie algebroids (groupoids), namely 2-term representations up to homotopy. Finally, it is well known that Lie groupoids are "concrete" incarnations of differentiable stack…