{"paper":{"title":"On Shimura's isomorphism and $(\\Gamma, G)$-bundles on the upper-half plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Claudio Meneses","submitted_at":"2015-11-03T00:37:54Z","abstract_excerpt":"For a compact real form $U$ of a complex simple Lie group $G$, and an irreducible representation $\\rho:\\Gamma \\to U$ of a Fuchsian group of the first kind $\\Gamma$, it is shown that the classical isomorphism of Shimura, for the periods of a cusp form of weight 2 with values in $\\mathfrak{g}$ and the representation $\\textrm{Ad}\\rho:\\Gamma\\to\\textrm{Aut}\\mathfrak{g}$, can be interpreted as the differential at a point of the zero section, for a natural map from the cotangent bundle of the moduli space of certain $(\\Gamma, G)$-bundles over $\\mathbb{H}$ (in the sense of Seshadri) to an open set in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00747","kind":"arxiv","version":3},"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"}