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Presentation of Borel subgroups of Kac-Moody groups over local rings

  • Robynn Corveleyn
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Abstract

We obtain presentations of Borel subgroups of certain Chevalley groups and Kac-Moody groups of simply laced type. More precisely, we show that Borel subgroups of simply laced Chevalley groups over a commutative, unital ring (satisfying a minor technical condition), are the amalgamated product of their rank 2 subgroups, generalising a result of Tits over fields (different from 𝔽2). We moreover show that Borel subgroups of Kac-Moody groups over local Bézout domains also have a presentation as an amalgamated product of their rank 2 subgroups as soon as this holds for their rank 3 subgroups. In particular we deduce that Borel subgroups of simply laced Kac-Moody groups over a local Bézout domain (with residue field different from 𝔽2) have such a presentation if and only if they are of 3-spherical type.

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Cite

BibTeXRIS
BibTeX
@misc{corveleyn2026presentation,
  title = {{Presentation of Borel subgroups of Kac-Moody groups over local rings}},
  author = {Robynn Corveleyn},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05224},
  eprint = {2610.05224},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05224},
}
RIS
TY  - UNPB
TI  - Presentation of Borel subgroups of Kac-Moody groups over local rings
AU  - Robynn Corveleyn
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05224
UR  - https://arxiv.org/abs/2610.05224
AB  - We obtain presentations of Borel subgroups of certain Chevalley groups and Kac-Moody groups of simply laced type. More precisely, we show that Borel subgroups of simply laced Chevalley groups over a commutative, unital ring (satisfying a minor technical condition), are the amalgamated product of their rank 2 subgroups, generalising a result of Tits over fields (different from 𝔽_2). We moreover show that Borel subgroups of Kac-Moody groups over local Bézout domains also have a presentation as an amalgamated product of their rank 2 subgroups as soon as this holds for their rank 3 subgroups. In particular we deduce that Borel subgroups of simply laced Kac-Moody groups over a local Bézout domain (with residue field different from 𝔽_2) have such a presentation if and only if they are of 3-spherical type.
ER  -