PreprintCC BY 4.0arXiv
A description of the canonical symplectic form of the cotangent bundle of a generalized flag manifold
Abstract
We investigate the symplectic geometry of homogeneous spaces associated with semisimple Lie groups, with particular emphasis on cotangent bundles of generalized flag manifolds. Our approach gives an explicit description of the Liouville symplectic form on these spaces in terms of the connections and curvature forms of principal bundles naturally arising from the Lie group structure. This provides a geometric link between the Lie-theoretic properties of generalized flag manifolds and the symplectic structures carried by their cotangent bundles.
Related
- Stability of the Cotangent Bundle on Surfaces with Ample Canonical Class
- A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle
- The Frohmanian Symplectic Tether: Canonical Uniqueness on Coadjoint Orbits of SDiff(T3), Non-Degenerate Casimir Coupling, and Conditional Global Regularity via Quartic Young Absorption in Lean 4
- Canonical and symplectic analysis of the Holst action in the G→ 0 limit
- The intersection of two real flag manifolds in a complex flag manifold, and the canonical form of a compact symmetric triad
BibTeX
@misc{fervenza2026description,
title = {{A description of the canonical symplectic form of the cotangent bundle of a generalized flag manifold}},
author = {Juan Fervenza and Lino Grama and Luiz A. B. San Martin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10902},
eprint = {2610.10902},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10902},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A description of the canonical symplectic form of the cotangent bundle of a generalized flag manifold
AU - Juan Fervenza
AU - Lino Grama
AU - Luiz A. B. San Martin
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10902
UR - https://arxiv.org/abs/2610.10902
AB - We investigate the symplectic geometry of homogeneous spaces associated with semisimple Lie groups, with particular emphasis on cotangent bundles of generalized flag manifolds. Our approach gives an explicit description of the Liouville symplectic form on these spaces in terms of the connections and curvature forms of principal bundles naturally arising from the Lie group structure. This provides a geometric link between the Lie-theoretic properties of generalized flag manifolds and the symplectic structures carried by their cotangent bundles.
ER -