{"paper":{"title":"The Brauer loop scheme and orbital varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Allen Knutson, Paul Zinn-Justin","submitted_at":"2010-01-19T18:59:35Z","abstract_excerpt":"A. Joseph invented multidegrees in [Jo84] to study orbital varieties, which are the components of an orbital scheme, itself constructed by intersecting a nilpotent orbit with a Borel subalgebra. Their multidegrees, known as Joseph polynomials, give a basis of a (Springer) representation of the Weyl group. In the case of the nilpotent orbit $\\{ M^2=0 \\}$, the orbital varieties can be indexed by noncrossing chord diagrams in the disc. In this paper we study the normal cone to the orbital scheme inside this nilpotent orbit $\\{ M^2 = 0 \\}$. This gives a better-motivated construction of the Brauer "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3335","kind":"arxiv","version":3},"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"}