论文标题
强大的传递性，穆法的状况和howe- moore属性
Strong transitivity, Moufang's condition and the Howe--Moore property
论文作者
论文摘要
首先，我们证明，每一个封闭的亚组$ h $ type-type type-type type type type type type type type type type type type type type type type type typers typersy厚的仿射建筑物$Δ$ dimension $ \ geq 2 $，在$Δ$上强烈过渡。如果此外$δ$不可约束，并且$ h $在拓扑上很简单，我们表明$ h $是$ k $ - 合理点的亚组$ \ g（k）^+$，与与非Archimean Localean Local Field $ k $相比，$ k $ \ g（k）$ \ g（k）$。其次，我们将\ cite {bm00b}中给出的证据概括为双期树木的情况下，将任何有限的厚厚的仿射建筑物$Δ$概括为$ \ aut（δ）$的任何拓扑简单，封闭，易于传递和类型的子组的任何有限厚的厚仿型。该证明与迄今为止文献中使用的策略不同，并且在极性分解$ ka^+k $上没有中继，其中$ k $是最大的紧凑型亚组，并且重要的事实是$ a^+$是Abelian最大的次级次级semi-Group。
Firstly, we prove that every closed subgroup $H$ of type-preserving automorphisms of a locally finite thick affine building $Δ$ of dimension $\geq 2$ that acts strongly transitively on $Δ$ is Moufang. If moreover $Δ$ is irreducible and $H$ is topologically simple, we show that $H$ is the subgroup $\G(k)^+$ of the $k$-rational points $\G(k)$ of the isotropic simple algebraic group $\G$ over a non-Archimedean local field $k$ associated with $Δ$. Secondly, we generalise the proof given in \cite{BM00b} for the case of bi-regular trees to any locally finite thick affine building $Δ$, and obtain that any topologically simple, closed, strongly transitive and type-preserving subgroup of $\Aut(Δ)$ has the Howe--Moore property. This proof is different than the strategy used so far in the literature and does not relay on the polar decomposition $KA^+K$, where $K$ is a maximal compact subgroup, and the important fact that $A^+$ is an abelian maximal sub-semi-group.
