{"paper":{"title":"The strong Macdonald conjecture and Hodge theory on the Loop Grassmannian","license":"","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Constantin Teleman, Ian Grojnowski, Susanna Fishel","submitted_at":"2004-11-16T19:26:24Z","abstract_excerpt":"We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology $H^q(X;\\Omega^p)$ of the loop Grassmannian X is freely generated by de Rham's forms on the disk coupled to algebra generators of $H*(BG)$. Equating Euler characteristics of the two gives an identity, independently known to Macdonald [M], which generalises Ramanujan's_1\\psi_1 sum. Simply laced root systems at level 1 are related to a `strong'_4\\psi_4 sum. Failure of Hodge decomposition implies the singularity of X, and of the algebraic loop gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411355","kind":"arxiv","version":1},"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"}