{"paper":{"title":"Exterior powers of the reflection representation in the cohomology of Springer fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anthony Henderson","submitted_at":"2010-01-18T23:21:17Z","abstract_excerpt":"Let $H^*(\\calB_e)$ be the cohomology of the Springer fibre for the nilpotent element $e$ in a simple Lie algebra $\\g$, on which the Weyl group $W$ acts by the Springer representation. Let $\\Lambda^i V$ denote the $i$th exterior power of the reflection representation of $W$. We determine the degrees in which $\\Lambda^i V$ occurs in the graded representation $H^*(\\calB_e)$, under the assumption that $e$ is regular in a Levi subalgebra and satisfies a certain extra condition which holds automatically if $\\g$ is of type A, B, or C. This partially verifies a conjecture of Lehrer--Shoji, and extends"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3164","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"}