{"paper":{"title":"Two character formulas for $\\hat{sl_2}$ spaces of coinvariants","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"B. Feigin, M. Jimbo, S. Loktev, T. Miwa","submitted_at":"2002-11-22T17:10:40Z","abstract_excerpt":"We consider $\\hat{sl_2}$ spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra $U(sl_2\\otimes\\C[t])$. The first one is generated by $sl_2\\otimes t^N$, and the second one is generated by $e\\otimes P(t), f\\otimes R(t)$ where $P(t), R(t)$ are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and $q$-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211354","kind":"arxiv","version":2},"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"}