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We show that these partitions can be better understood by constructing cell decompositions of a product of two Bott-Samelson varieties Z_{u, v}, where u and v are sequences of simple reflections. We construct coordinates on each cell of the decompositions and in the case of a positive subexpression, we relate these coordinates to regular functions on a p"},"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":"1310.4642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-17T10:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"117675628348056e33abc323688167dc6c50f2b8cacd190918394b2ca95849d7","abstract_canon_sha256":"3db14dd9a9f18f6d5125617232bd8c612d5ecfbe470914fe0db6f4db35712970"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:54.246735Z","signature_b64":"zOpyR1kL5URV/28b0HP6Gypn2rHOgcjACWGvYRbncbts7WIsIF2E9duZ+7JZUxAKTk/uE9zI9WzObj2reTouDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ec313c0873e3252c46ba0e14b1c5e10c2aa4cf63a7e03033646c7e9b9ce2cd2","last_reissued_at":"2026-05-18T03:06:54.246084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:54.246084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cell decompositions of double Bott-Samelson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Victor Mouquin","submitted_at":"2013-10-17T10:04:15Z","abstract_excerpt":"Let G be a connected complex semisimple Lie group. 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