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We classify all special unipotent representations of $G$ attached to $\\check{\\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. When $\\check{\\mathcal O}$ has good parity in the sense of Moeglin, we construct all such representations of $G$ via the method of theta lifting. As a consequence of the construction and the classification, we conclude tha"},"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":"1712.05552","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-15T06:15:52Z","cross_cats_sorted":[],"title_canon_sha256":"6623dd7024e4ba38558d07a7847c8e15028c2ae5bd083d57f0698c7fbedae7fe","abstract_canon_sha256":"1325ec4483327159fcf0d11567e5fc6583c385dd222c9960a670dc5d90222b8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:03.969925Z","signature_b64":"hqCaNfZn3xshgqJtonPm/wFVw0FtyQZZ4aqnNvvNi8m8LkXEDyVhJCxpVl9EXO64I6dxzGERvN9Xf/nPPIoOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a0b8eca4732046527c98587e33dde6418b44df467e00ceffac782e89c0d78c","last_reissued_at":"2026-07-05T10:16:03.969408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:03.969408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special unipotent representations of real classical groups: construction and unitarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Binyong Sun, Chen-bo Zhu, Dan Barbasch, Jia-Jun Ma","submitted_at":"2017-12-15T06:15:52Z","abstract_excerpt":"Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\\check{\\mathcal O}$ of $\\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We classify all special unipotent representations of $G$ attached to $\\check{\\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. When $\\check{\\mathcal O}$ has good parity in the sense of Moeglin, we construct all such representations of $G$ via the method of theta lifting. 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