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Precisely, let $\\widetilde{G_0} =\\widetilde{Spin}(a,b)$ with $a+b=2n$, the nonlinear double cover of $Spin(a,b)$, and let $\\widetilde{K}=Spin(a, \\mathbb C)\\times Spin(b, \\mathbb C)$ be the complexification of the maximal compact subgroup of $\\widetilde{G_0}$. We consider the nilpotent orbit $\\mathcal O_c$ parametrized by $[3 \\ 2^{2k} \\ 1^{2n-4k-3}]$ with $k>0$. We provide a list of unipotent representations that are genuine, and prove that 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":"1702.04841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-02-16T02:14:44Z","cross_cats_sorted":[],"title_canon_sha256":"50bb4087cda5d1af42b52990958e35b647f5e54ce9991276b98b79a254f88721","abstract_canon_sha256":"4980e3444564efb14d920cbe4e8270ff10e5072337c59cf81dc48c21c3474f75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:03.544035Z","signature_b64":"jxLhxhQfv3zv6mr+YAs/y+IQyHMW0xlZD6Wa89pBj6vQJWkZhU2+mFRrpFwVOoJaruzpyVtK5lTcJuY9Hv+MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2639f1310f5aa986ed02b9c306dba5d26c9b4cda7af103a8ecd223e11ce919af","last_reissued_at":"2026-05-18T00:36:03.543586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:03.543586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations associated to small nilpotent orbits for real Spin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dan Barbasch, Wan-Yu Tsai","submitted_at":"2017-02-16T02:14:44Z","abstract_excerpt":"The results in this paper provide a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits. Precisely, let $\\widetilde{G_0} =\\widetilde{Spin}(a,b)$ with $a+b=2n$, the nonlinear double cover of $Spin(a,b)$, and let $\\widetilde{K}=Spin(a, \\mathbb C)\\times Spin(b, \\mathbb C)$ be the complexification of the maximal compact subgroup of $\\widetilde{G_0}$. We consider the nilpotent orbit $\\mathcal O_c$ parametrized by $[3 \\ 2^{2k} \\ 1^{2n-4k-3}]$ with $k>0$. 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