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We study the cohomological equation for discrete parabolic actions on $\\mathbb G$ via representation theory. Specifically, we characterize the obstructions to solving the cohomological equation and construct smooth solutions with Sobolev estimates. We prove that global estimates of the solution are generally not tame, and our non-tame estimates in the case $\\mathbb G=SL(n,\\mathbb R)$ are sharp up t"},"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":"1809.03021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"9a13aa8db25a97a7adc681fef12d81c1f5692c405fda1c6dc7327f092cd33d96","abstract_canon_sha256":"fdd99fc560b7587260fab9d8fb7efda9d4419498135b734457be6ff82384b1b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:13.585565Z","signature_b64":"g2R8YLEoQYKU0jpb8RvAuq2Dp97CGpGF321Oh6tCgczIBBkyA9uYSyvs9bc2I288c5mkTpzC8VWzaLiuu2NeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","last_reissued_at":"2026-05-18T00:05:13.584656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:13.584656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomological equation and cocycle rigidity of discrete parabolic actions in some higher rank Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"James Tanis, Zhenqi Jenny Wang","submitted_at":"2018-09-09T18:41:31Z","abstract_excerpt":"Let $\\mathbb{G}$ denote a higher rank $\\mathbb R$-split simple Lie group of the following type: $SL(n,\\mathbb R)$, $SO_o(m,m)$, $E_{6(6)}$, $E_{7(7)}$ and $E_{8(8)}$, where $m\\geq 4$ and $n \\geq 3$. 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