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For such a Lie group $G$, we can find a parabolic subgroup $P=MAN$, with given Langlands decomposition, such that $N$ is abelian, and $N$ admits a generic character with compact stabilizer. We will call any parabolic subgroup $P$ satisfying this properties a Siegel parabolic.\n  Let $(\\pi,V)$ be an admissible, smooth, Fr\\'echet representation of a Lie group of tube type $G$, and let $P \\subset G$ b"},"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":"1211.5879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T08:19:33Z","cross_cats_sorted":[],"title_canon_sha256":"490fd88a2c1bdffd5633f0ba6425236bb64d23af040b63ac3401afaf1acde3b9","abstract_canon_sha256":"d0e8a38a8597829551e8dbe20220d8edb35c3b203d95598a3e4172676d7a15d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:01.721126Z","signature_b64":"t2+sKSCdHc8Izbv/LyXwrkAcETfbSNIzPUAVwNzXuswYWCblXWnWR1uhMxi0Qb8UNXme8vJ8IazYvX6wxDc4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"412cb8a1e510e656a19a426b9fca5f0d630a18e44f1bb1ff4e8469b0b0082f0c","last_reissued_at":"2026-05-18T03:40:01.720724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:01.720724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bessel-Plancherel theorem and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Raul Gomez","submitted_at":"2012-11-26T08:19:33Z","abstract_excerpt":"Let $G$ be a simple Lie Group with finite center, and let $K\\subset G$ be a maximal compact subgroup. 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