{"paper":{"title":"The $\\mathfrak{sl}_\\infty$-crystal combinatorics of higher level Fock spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Emily Norton, Thomas Gerber","submitted_at":"2017-04-07T10:22:47Z","abstract_excerpt":"For integers $e,\\ell\\geq 2$, the level $\\ell$ Fock space has an $\\mathfrak{sl}_\\infty$-crystal structure arising from the action of a Heisenberg algebra, intertwining the $\\widehat{\\mathfrak{sl}_e}$-crystal. The vertices of these crystals are charged $\\ell$-partitions. We give the combinatorial rule for computing the arrows anywhere in the $\\mathfrak{sl}_\\infty$-crystal. This allows us to pinpoint the location of any charged $\\ell$-partition. As an application, we compute the support of the spherical representation of a cyclotomic rational Cherednik algebra, and in particular, the set of param"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02169","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"}