{"paper":{"title":"Explicit Demazure character formula for negative dominant characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"S. Senthamarai Kannan","submitted_at":"2012-11-15T09:29:49Z","abstract_excerpt":"In this paper, we prove that for any semisimple simply connected algebraic group $G$, for any regular dominant character $\\lambda$ of a maximal torus $T$ of $G$ and for any element $\\tau$ in the Weyl group $W$, the character $e^{\\rho}\\cdot char(H^{0}(X(\\tau), \\mathcal{L}_{\\lambda-\\rho}))$ is equal to the sum $\\sum_{w\\leq \\tau}char(H^{l(w)}(X(w),\\mathcal{L}_{-\\lambda}))^{*})$ of the characters of dual of the top cohomology modules on the Schubert varieties $X(w)$, $w$ running over all elements satisfying $w\\leq \\tau$. Using this result, we give a basis of the intersection of the Kernels of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3542","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"}