---
_id: '66303'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Andreas
  full_name: Gross, Andreas
  last_name: Gross
- first_name: Arne
  full_name: Kuhrs, Arne
  last_name: Kuhrs
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Dmitry
  full_name: Zakharov, Dmitry
  last_name: Zakharov
citation:
  ama: Gross A, Kuhrs A, Ulirsch M, Zakharov D. Tropical reductive groups and principal
    bundles on metric graphs. <i>arXiv:251105422</i>. Published online 2025.
  apa: 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>.
  bibtex: '@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}
    }'
  chicago: Gross, Andreas, Arne Kuhrs, Martin Ulirsch, and Dmitry Zakharov. “Tropical
    Reductive Groups and Principal Bundles on Metric Graphs.” <i>ArXiv:2511.05422</i>,
    2025.
  ieee: A. Gross, A. Kuhrs, M. Ulirsch, and D. Zakharov, “Tropical reductive groups
    and principal bundles on metric graphs,” <i>arXiv:2511.05422</i>. 2025.
  mla: Gross, Andreas, et al. “Tropical Reductive Groups and Principal Bundles on
    Metric Graphs.” <i>ArXiv:2511.05422</i>, 2025.
  short: A. Gross, A. Kuhrs, M. Ulirsch, D. Zakharov, ArXiv:2511.05422 (2025).
date_created: 2026-07-08T06:18:46Z
date_updated: 2026-07-08T06:19:02Z
external_id:
  arxiv:
  - '2511.05422'
language:
- iso: eng
publication: arXiv:2511.05422
status: public
title: Tropical reductive groups and principal bundles on metric graphs
type: preprint
user_id: '82981'
year: '2025'
...