{"paper":{"title":"Spin nilHecke algebras of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian Johnson, Weiqiang Wang","submitted_at":"2017-06-20T02:18:43Z","abstract_excerpt":"We formulate and study the spin nilHecke algebras ${}^\\mathfrak{b}\\!{\\mathrm{NH}}_n^-$ and ${}^\\mathfrak{d}\\!{\\mathrm{NH}}_n^-$ of type B/D, which differ from the usual nilHecke algebras by some odd signs. The type B spin nilHecke algebra is a nil version of the spin type B Hecke algebra introduced earlier by the second author and Khongsap, but not for the type D one. We construct faithful polynomial representations $\\mathrm{Pol}_n^-$ of the nilHecke algebras via odd Demazure operators. We formulate the spin Schubert polynomials, and use them to show that the spin nilHecke algebras are matrix "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06240","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"}