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Consider the set $Max Hom(V,\\tilde{V})$ of full rank elements in $Hom(V,\\tilde{V})$, and the nilpotent orbit correspondence $\\mathcal{O} \\subset \\mathfrak{g}$ and $\\Theta (\\mathcal{O})\\subset \\tilde{\\mathfrak{g}}$ induced by elements of $Max Hom(V,\\tilde{V})$ via the moment maps. Let $(\\pi,\\mathscr{V})$ be a smooth irreducible representation of $G$. We show that there is a correspondence of the generali"},"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":"1302.3744","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-15T12:52:52Z","cross_cats_sorted":[],"title_canon_sha256":"608b5f5750af5f19c947588e330c5b2681c56dd1405f95cf51893589d3dcdfdc","abstract_canon_sha256":"1ecd7703bec18119fd5109a3472a281fde5c2e5814fced69cff0c7f486b4b940"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:49.977197Z","signature_b64":"K0rScOGTIOBy0zDbvFamUHE7HQ5KvKtjUkdI3s3+MjiNUco8IPlm4T98SSaFFX4WXlmIkZlxBjT4D9ltEKIKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cec7a1a68c9f6a5bd0754a969b23738b2c5133f9964e8bcf34104e9a5f8d6fa9","last_reissued_at":"2026-05-18T03:14:49.976330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:49.976330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local theta lifting of generalized Whittaker models associated to nilpotent orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chen-bo Zhu, Raul Gomez","submitted_at":"2013-02-15T12:52:52Z","abstract_excerpt":"Let $(G,\\tilde{G})$ be a reductive dual pair over a local field ${\\Fontauri k}$ of characteristic 0, and denote by $V$ and $\\tilde{V}$ the standard modules of $G$ and $\\tilde{G}$, respectively. Consider the set $Max Hom(V,\\tilde{V})$ of full rank elements in $Hom(V,\\tilde{V})$, and the nilpotent orbit correspondence $\\mathcal{O} \\subset \\mathfrak{g}$ and $\\Theta (\\mathcal{O})\\subset \\tilde{\\mathfrak{g}}$ induced by elements of $Max Hom(V,\\tilde{V})$ via the moment maps. Let $(\\pi,\\mathscr{V})$ be a smooth irreducible representation of $G$. 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