{"paper":{"title":"Affine Geometric Crystal of $A^{(1)}_n$ and Limit of Kirillov-Reshetikhin Perfect Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Kailash C. Misra, Toshiki Nakashima","submitted_at":"2016-08-22T06:56:12Z","abstract_excerpt":"Let $\\mathfrak g$ be an affine Lie algebra with index set $I = \\{0, 1, 2, \\cdots , n\\}$ and ${\\mathfrak g}^L$ be its Langlands dual. It is conjectured by Kashiwara et al.([16]) that for each $k \\in I \\setminus \\{0\\}$ the affine Lie algebra $\\mathfrak g$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for ${\\mathfrak g}^L$. Motivated by this conjecture we construct a positive geometric crystal for the affine Lie algebra ${\\mathfrak g}= A^{(1)}_n$ for each Dynkin index $k\\in I\\setminus\\{0\\}$ and show that its u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06063","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"}