PreprintCC BY 4.0arXiv
Parabolic Lie algebroid connections on parabolic principal bundles over curves
Abstract
Let X be a compact connected Riemann surface and S ⊂ X a finite subset. We consider parabolic principal G--bundles ℰG on X with parabolic structure on S, where G is a connected complex reductive affine algebraic group. Let P ⊂ G be a parabolic subgroup and ℰP ⊂ ℰG a reduction of structure group of ℰG to P. We give a criterion for the existence of a parabolic Lie algebroid connection on ℰP for any given parabolic Lie algebroid on (X, S) whose anchor map is not surjective. More precisely, ℰP admits a parabolic Lie algebroid connection if the reduction ℰP ⊂ ℰG is parabolically infinitesimally rigid. In particular, the Harder--Narasimhan reduction of ℰG admits a parabolic Lie algebroid connection.
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BibTeX
@misc{biswas2026parabolic,
title = {{Parabolic Lie algebroid connections on parabolic principal bundles over curves}},
author = {Indranil Biswas and Pritthijit Biswas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01402},
eprint = {2609.01402},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01402},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parabolic Lie algebroid connections on parabolic principal bundles over curves
AU - Indranil Biswas
AU - Pritthijit Biswas
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01402
UR - https://arxiv.org/abs/2609.01402
AB - Let X be a compact connected Riemann surface and S ⊂ X a finite subset. We consider parabolic principal G--bundles ℰ_G on X with parabolic structure on S, where G is a connected complex reductive affine algebraic group. Let P ⊂ G be a parabolic subgroup and ℰ_P ⊂ ℰ_G a reduction of structure group of ℰ_G to P. We give a criterion for the existence of a parabolic Lie algebroid connection on ℰ_P for any given parabolic Lie algebroid on (X, S) whose anchor map is not surjective. More precisely, ℰ_P admits a parabolic Lie algebroid connection if the reduction ℰ_P ⊂ ℰ_G is parabolically infinitesimally rigid. In particular, the Harder--Narasimhan reduction of ℰ_G admits a parabolic Lie algebroid connection.
ER -