{"paper":{"title":"Multi-dimensional Weyl Modules and Symmetric Functions","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"B. Feigin, S. Loktev","submitted_at":"2002-12-01T10:13:50Z","abstract_excerpt":"The Weyl modules in the sense of V.Chari and A.Pressley [CP] over the current Lie algebra on an affine variety are studied. We show that local Weyl modules are finite-dimensional and generalize the tensor product decomposition theorem from [CP].\n  More explicit results are stated for currents on a non-singular affine variety of dimension $d$ with coefficients in the Lie algebra $sl_r$. The Weyl modules with highest weights proportional to the vector representation one are related to the multi-dimensional analogs of harmonic functions. The dimensions of such local Weyl modules are calculated in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212001","kind":"arxiv","version":4},"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"}