@article{66316,
  abstract     = {{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.}},
  author       = {{Gross, Andreas and Ulirsch, Martin and Zakharov, Dmitry}},
  journal      = {{arXiv:2206.10219}},
  title        = {{{Principal bundles on metric graphs: the $\mathrm{GL}_n$ case}}},
  doi          = {{10.1016/j.aim.2022.108775}},
  year         = {{2022}},
}