Positively ratioed representations
Positively ratioed representations
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正比表示
DOI：
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发表时间：
2016
影响因子：
0.9
通讯作者：
Tengren Zhang
中科院分区：
文献类型：
--
作者：
Giuseppe Martone;Tengren Zhang
设S是亏格至少为2的可定向闭曲面，G是非紧型半单真实的代数群。我们考虑一类从S到G的基本群的表示，称为正比例表示。这些是带有附加条件的Anosov表示，即某些相关的交比满足正性性质。这种表示的例子包括希钦表示和极大表示。使用测地电流，我们表明，这些积极的比例表示相应的长度函数是良好的行为。特别是，我们证明了收缩不等式，所有这些积极的ratioed表示。
Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain associated cross ratios satisfy a positivity property. Examples of such representations include Hitchin representations and maximal representations. Using geodesic currents, we show that the corresponding length functions for these positively ratioed representations are well-behaved. In particular, we prove a systolic inequality that holds for all such positively ratioed representations.