{"paper":{"title":"Integrable crystals and restriction to Levi via generalized slices in the affine Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Vasily Krylov","submitted_at":"2017-09-01T16:53:03Z","abstract_excerpt":"Let $G$ be a connected reductive algebraic group over $\\mathbb{C}$. Let $\\Lambda^{+}_{G}$ be the monoid of dominant weights of $G$. We construct the integrable crystals $\\mathbf{B}^{G}(\\lambda),\\ \\lambda\\in\\Lambda^{+}_{G}$, using the geometry of generalized transversal slices in the affine Grassmannian of the Langlands dual group. We construct the tensor product maps $\\mathbf{p}_{\\lambda_{1},\\lambda_{2}}\\colon \\mathbf{B}^{G}(\\lambda_{1}) \\otimes \\mathbf{B}^{G}(\\lambda_{2}) \\rightarrow \\mathbf{B}^{G}(\\lambda_{1}+\\lambda_{2})\\cup\\{0\\}$ in terms of multiplication of generalized transversal slices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00391","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"}