论文标题
径向快速衰减并不意味着快速衰减
Radial rapid decay does not imply rapid decay
论文作者
论文摘要
我们为径向快速衰减特性提供了新的动力标准。我们详细介绍了组$γ的特殊情况：= \ Mathbf {sl} _2（a）$，其中$ a：= \ m athbb {f} _q [x，x，x^{ - 1}] $是laurent多项式的环，具有$ \ m i \ m i \ nsution的$ \ mathbb {$ ntuctiation两棵树的产物，以表明具有径向快速衰减（RRD）特性，并且没有快速衰减（RD）特性。该标准还适用于半圣躺式组中的不可约定的晶格，其有限的中心具有借助Finsler指标定义的长度函数。这些示例回答了Chatterji和Chatterji问的一个问题，此外表明，与RD属性不同，RRD属性不是开放子组继承的。
We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $Γ:= \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with coefficients in $\mathbb{F}_q$, endowed with the length function coming from a natural action of $Γ$ on a product of two trees, to show that is has the radial rapid decay (RRD) property and doesn't have the rapid decay (RD) property. The criterion also applies to irreducible lattices in semisimple Lie groups with finite center endowed with a length function defined with the help of a Finsler metric. These examples answer a question asked by Chatterji and moreover show that, unlike the RD property, the RRD property isn't inherited by open subgroups.
