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Consider a quotient Ore domain of the lower nilpotent part of a quantized universal enveloping algebra of arbitrary symmetrizable Kac-Moody type. Then non-integral powers of the image of the Chevalley generators generate the quantized q-analogue of the birational Weyl group action. Using the same method, we shall reconstruct the quantized B\\\"acklu"},"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":"0808.2604","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-08-19T14:53:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7321f84b9ec4d1a263888bd8494884d3dba7cc4c0cda8bdeee5299db089a38d7","abstract_canon_sha256":"9114297b4aea734da9389c6c88c191c06c5720938bfbe1a1472cd48a97ac3ecb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.936129Z","signature_b64":"Jls5AT88wNycjku4dOPH/k/gBXcaXsiZYHAmd13XhaOx8EPlPIAYQyCDp8AERnEPus30hCBEsqFSSaZspv8PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e8037cb094d870811ae613d4eec31d531757c050eebd7abfc74adcbd501d6a","last_reissued_at":"2026-05-18T04:07:06.935447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.935447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum groups and quantization of Weyl group symmetries of Painlev\\'e systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Gen Kuroki","submitted_at":"2008-08-19T14:53:54Z","abstract_excerpt":"We shall construct the quantized q-analogues of the birational Weyl group actions arising from nilpotent Poisson algebras, which are conceptual generalizations, proposed by Noumi and Yamada, of the B\\\"acklund transformations for Painlev\\'e equations. 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