Generic Properties of Hitchin Representations
| Autor: | Jung, Hongtaek |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a split real form of a complex simple adjoint group and let $S$ be a closed orientable surface of genus at least 2. We show that for generic $\operatorname{PSL}_{2k-1}(\mathbb{R})$-Hitchin representations $\rho$, the middle eigenvalue of $\rho(x)$ is not equal to 1 for all non-trivial elements $x\in \pi_1(S)$. Using the same technique, we prove that the set of strongly dense $G$-Hitchin representations is generic. This generalizes the result of Long, Reid and Wolff for the $G=\operatorname{PSL}_n(\mathbb{R})$ case. Comment: 17 pages, 2 figures. Comments welcome |
| Databáze: | arXiv |
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