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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.06063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-08-22T06:56:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"82030551c1e4cda1f4bfeea70ebea56f8c19a0cff90dca93ab0e226e502dd5e8","abstract_canon_sha256":"79cbf5f060ba99b636dc173d8d030b1f538333b38e51f722dd8a7b016a47cd0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:22.403399Z","signature_b64":"hZLOyHakl4xRQHgNMHsDIREWMZ8d/Uw+yiPAgWpa8DKQZaT8USArOflF35dj49GWgkOCEcBrQVZcjwXI9HLUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8963effa4b849b61b1248f84cadca5eb198e4220482539427497e6f1200ef2cb","last_reissued_at":"2026-05-18T01:08:22.402867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:22.402867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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