Principal bundles on metric graphs: the $\mathrm{GL}_n$ case Gross, Andreas Ulirsch, Martin Zakharov, Dmitry 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 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66316 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2022.108775 info:eu-repo/semantics/altIdentifier/arxiv/2206.10219 info:eu-repo/semantics/closedAccess