论文标题
Zariski致密的表面基团在分裂真实谎言基团的不均匀晶格中
Zariski-dense surface groups in non-uniform lattices of split real Lie groups
论文作者
论文摘要
对于$ \ textrm {sl}（n，\ mathbb {r}）$（$ n \ geq3 $），$ \ textrm {so}（n+1，n）$（$ n \ geq2 $），$ \ \ \ \ \ \ \ \ textrm {sp} $ \ textrm {g} _2 $，我们展示了非均匀的晶格，其中我们通过算术方法构造了薄的希钦表示。这些表示形式在映射类组的动作下提供了无限的轨道（除了$ \ textrm {g} _2 $）。特别是，我们表明，当$ p \ neq2 $是$ \ mathrm {sl}的每个非均匀晶格时
For $\textrm{SL}(n,\mathbb{R})$ ($n\geq3$), $\textrm{SO}(n+1,n)$ ($n\geq2$), $\textrm{Sp}(2n,\mathbb{R})$ ($n\geq2$) and for the adjoint real split form of the exceptional group $\textrm{G}_2$, we exhibit non-uniform lattices in which we construct thin Hitchin representations by arithmetic methods. These representations give infinitely many orbits under the action of the mapping class group (except maybe for $\textrm{G}_2$). In particular, we show that when $p\neq2$ is prime every non-uniform lattice of $\mathrm{SL}(p,\mathbb{R})$ contains thin Hitchin representations.
