{"paper":{"title":"A note on the symplectic structure on the space of G-monopoles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov, Ivan Mirkovi\\'c, Michael Finkelberg, Nikita Markarian","submitted_at":"1998-03-25T19:28:35Z","abstract_excerpt":"Let $G$ be a semisimple complex Lie group with a Borel subgroup $B$. Let $X=G/B$ be the flag manifold of $G$. Let $C=P^1\\ni\\infty$ be the projective line. Let $\\alpha\\in H_2(X,{\\Bbb Z})$. The moduli space of $G$-monopoles of topological charge $\\alpha$ (see e.g. [Jarvis]) is naturally identified with the space $M_b(X,\\alpha)$ of based maps from $(C,\\infty)$ to $(X,B)$ of degree $\\alpha$. The moduli space of $G$-monopoles carries a natural hyperk\\\"ahler structure, and hence a holomorphic symplectic structure. We propose a simple explicit formula for the symplectic structure on $M_b(X,\\alpha)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803124","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}