Superrigidity for representations of transverse measured groupoids
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912976595845120 |
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| author | Sarti, Filippo Savini, Alessio |
| author_facet | Sarti, Filippo Savini, Alessio |
| contents | For $i=1,\ldots,k$, let $\mathbf{G}_i$ be a connected, simply connected, semisimple algebraic group over some local field $κ_i$ of characteristic zero. Let $G_i=\mathbf{G}_i(κ_i)$ be the $κ_i$-points of $\mathbf{G}_i$ and denote by $G=\prod_{i=1}^k G_i$. If we assume that $G$ has higher rank and each factor has positive rank, given an ergodic transverse $G$-system $(X,μ,Y)$, we prove a superrigidity phenomenon for Zariski dense representations of the transverse groupoid $(G \ltimes X)|_Y$ into either an almost simple or a reductive algebraic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Superrigidity for representations of transverse measured groupoids Sarti, Filippo Savini, Alessio Dynamical Systems Group Theory For $i=1,\ldots,k$, let $\mathbf{G}_i$ be a connected, simply connected, semisimple algebraic group over some local field $κ_i$ of characteristic zero. Let $G_i=\mathbf{G}_i(κ_i)$ be the $κ_i$-points of $\mathbf{G}_i$ and denote by $G=\prod_{i=1}^k G_i$. If we assume that $G$ has higher rank and each factor has positive rank, given an ergodic transverse $G$-system $(X,μ,Y)$, we prove a superrigidity phenomenon for Zariski dense representations of the transverse groupoid $(G \ltimes X)|_Y$ into either an almost simple or a reductive algebraic group. |
| title | Superrigidity for representations of transverse measured groupoids |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2603.20548 |