{"paper":{"title":"Irreducible representations of rational Cherednik algebras for exceptional Coxeter groups, part II: some decomposition matrices of $H_c(E_8)$ and $H_c(F_4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Emily Norton","submitted_at":"2016-12-23T20:25:25Z","abstract_excerpt":"This paper contains the decomposition matrices for blocks of defect at most $2$ in Category $\\mathcal{O}_c(W)$ of the rational Cherednik algebra when $W=E_8$ or $F_4$ with equal parameters $c=1/d$, $d>2$ a regular number of $W$. A corollary of the result is a classification of the dimensions of support of the irreducible modules $L(\\tau)$ in $\\mathcal{O}_{1/d}(W)$ except in the following cases: $W=E_8$, $d=4$ or $6$ and $L(\\tau)$ is in the principal block, or $d=2$ or $3$; $W=F_4$, $d=2$. In particular, this classifies the finite-dimensional modules of $H_c(E_8)$ when $d\\neq 2,3,4,6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08080","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"}