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Isomorphisms between Schwartz spaces under Vinberg's condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RT"],"primary_cat":"math.FA","authors_text":"Fulvio Ricci, Oksana Yakimova, Veronique Fischer","submitted_at":"2012-10-30T11:11:52Z","abstract_excerpt":"Let (N,K) be a nilpotent Gelfand pair, i.e., N is a nilpotent Lie group, K a compact group of automorphisms of N, and the algebra D(N)^K of left-invariant and K-invariant differential operators on N is commutative. In these hypotheses, N is necessarily of step at most two. We say that (N,K) satisfies Vinberg's condition if K acts irreducibly on $n/[n,n]$, where n= Lie(N).\n  Fixing a system D of d formally self-adjoint generators of D(N)^K, the Gelfand spectrum of the commutative convolution algebra L^1(N)^K can be canonically identified with a closed subset S_D of R^d. We prove that, on a nilp"},"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":"1210.7962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-30T11:11:52Z","cross_cats_sorted":["math.AC","math.RT"],"title_canon_sha256":"d1653a1a4a634eadf24c26ea163ef99d56e2a824876519d5a248f43b6c6d957e","abstract_canon_sha256":"1b8869c5913e827344bd314f25ee720ffff93ed0e582a62d2bfc6b90eb121075"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:57.506820Z","signature_b64":"gvce462BTz9hOYzzWeTBMSwgL24zHtUC484ZGm/ejBgsDyzy4BQl0SEvYkyzQtWljtFsMYLtMP8kz2hqJvh8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bca61f7797ebd99cd499360fd7b0cd967d1a045f319fb4198be567ad1426d63e","last_reissued_at":"2026-05-18T03:41:57.506204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:57.506204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nilpotent Gelfand pairs and spherical transforms of Schwartz functions III. 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