article Andreas Gross author Martin Ulirsch author 114697 Dmitry Zakharov author Using the notion of a root datum of a reductive group $G$ we propose a tropical analogue of a principal $G$-bundle on a metric graph. We focus on the case $G=\mathrm{GL}_n$, i.e. the case of vector bundles. Here we give a characterization of vector bundles in terms of multidivisors and use this description to prove analogues of the Weil--Riemann--Roch theorem and the Narasimhan--Seshadri correspondence. We proceed by studying the process of tropicalization. In particular, we show that the non-Archimedean skeleton of the moduli space of semistable vector bundles on a Tate curve is isomorphic to a certain component of the moduli space of semistable tropical vector bundles on its dual metric graph. 2022 eng 2206.1021910.1016/j.aim.2022.108775 Gross, Andreas, et al. “Principal Bundles on Metric Graphs: The $\mathrm{GL}_n$ Case.” <i>ArXiv:2206.10219</i>, 2022, doi:<a href="https://doi.org/10.1016/j.aim.2022.108775">10.1016/j.aim.2022.108775</a>. Gross A, Ulirsch M, Zakharov D. Principal bundles on metric graphs: the $\mathrm{GL}_n$ case. <i>arXiv:220610219</i>. Published online 2022. doi:<a href="https://doi.org/10.1016/j.aim.2022.108775">10.1016/j.aim.2022.108775</a> @article{Gross_Ulirsch_Zakharov_2022, title={Principal bundles on metric graphs: the $\mathrm{GL}_n$ case}, DOI={<a href="https://doi.org/10.1016/j.aim.2022.108775">10.1016/j.aim.2022.108775</a>}, journal={arXiv:2206.10219}, author={Gross, Andreas and Ulirsch, Martin and Zakharov, Dmitry}, year={2022} } Gross, A., Ulirsch, M., &#38; Zakharov, D. (2022). Principal bundles on metric graphs: the $\mathrm{GL}_n$ case. <i>ArXiv:2206.10219</i>. <a href="https://doi.org/10.1016/j.aim.2022.108775">https://doi.org/10.1016/j.aim.2022.108775</a> A. Gross, M. Ulirsch, and D. Zakharov, “Principal bundles on metric graphs: the $\mathrm{GL}_n$ case,” <i>arXiv:2206.10219</i>, 2022, doi: <a href="https://doi.org/10.1016/j.aim.2022.108775">10.1016/j.aim.2022.108775</a>. A. Gross, M. Ulirsch, D. Zakharov, ArXiv:2206.10219 (2022). Gross, Andreas, Martin Ulirsch, and Dmitry Zakharov. “Principal Bundles on Metric Graphs: The $\mathrm{GL}_n$ Case.” <i>ArXiv:2206.10219</i>, 2022. <a href="https://doi.org/10.1016/j.aim.2022.108775">https://doi.org/10.1016/j.aim.2022.108775</a>. 663162026-07-08T06:42:43Z2026-07-08T09:35:05Z