preprint Andreas Gross author Arne Kuhrs author Martin Ulirsch author 114697 Dmitry Zakharov author We propose an elementary tropical analogue of a reductive group that combines the datum of a Weyl group and the tropicalization of a fixed maximal torus. For the classical groups, as well as $G_2$, these tropical reductive groups admit descriptions as tropical matrix groups that resemble their classical counterparts. Employing this perspective, we introduce tropical principal bundles on metric graphs and study their explicit presentations as pushforwards of line bundles along covers with symmetries and extra data. Our main result identifies the essential skeleton of the moduli space of semistable principal bundles on a Tate curve with its tropical analogue. 2025 eng 2511.05422 @article{Gross_Kuhrs_Ulirsch_Zakharov_2025, title={Tropical reductive groups and principal bundles on metric graphs}, journal={arXiv:2511.05422}, author={Gross, Andreas and Kuhrs, Arne and Ulirsch, Martin and Zakharov, Dmitry}, year={2025} } Gross A, Kuhrs A, Ulirsch M, Zakharov D. Tropical reductive groups and principal bundles on metric graphs. <i>arXiv:251105422</i>. Published online 2025. Gross, Andreas, et al. “Tropical Reductive Groups and Principal Bundles on Metric Graphs.” <i>ArXiv:2511.05422</i>, 2025. Gross, Andreas, Arne Kuhrs, Martin Ulirsch, and Dmitry Zakharov. “Tropical Reductive Groups and Principal Bundles on Metric Graphs.” <i>ArXiv:2511.05422</i>, 2025. A. Gross, A. Kuhrs, M. Ulirsch, D. Zakharov, ArXiv:2511.05422 (2025). A. Gross, A. Kuhrs, M. Ulirsch, and D. Zakharov, “Tropical reductive groups and principal bundles on metric graphs,” <i>arXiv:2511.05422</i>. 2025. Gross, A., Kuhrs, A., Ulirsch, M., &#38; Zakharov, D. (2025). Tropical reductive groups and principal bundles on metric graphs. In <i>arXiv:2511.05422</i>. 663032026-07-08T06:18:46Z2026-07-08T06:19:02Z