{"paper":{"title":"Hecke Operators on Vector-Valued Modular Forms","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.NT","authors_text":"Aniket Joshi, Thomas Creutzig, Vincent Bouchard","submitted_at":"2018-07-20T03:19:51Z","abstract_excerpt":"We study Hecke operators on vector-valued modular forms for the Weil representation $\\rho_L$ of a lattice $L$. We first construct Hecke operators $\\mathcal{T}_r$ that map vector-valued modular forms of type $\\rho_L$ into vector-valued modular forms of type $\\rho_{L(r)}$, where $L(r)$ is the lattice $L$ with rescaled bilinear form $(\\cdot, \\cdot)_r = r (\\cdot, \\cdot)$, by lifting standard Hecke operators for scalar-valued modular forms using Siegel theta functions. The components of the vector-valued Hecke operators $\\mathcal{T}_r$ have appeared in [Comm. Math. Phys. 350 (2017), 1069-1121] as g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07703","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"}