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Precisely, let $ G_ 0 =Spin(2n,\\mathbb C)$ be the Spin complex group viewed as a real group, and $K\\cong G_0$ be the complexification of the maximal compact subgroup of $G_0$. We compute $K$-spectra of the regular functions on some small nilpotent orbits $\\mathcal O$ transforming according to characters $\\psi$ of $C_{ K}(\\mathcal O)$ trivial on the connected component of the identity $C_{ K}(\\mathcal O)^0$. We then match the"},"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":"1702.08223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-02-27T10:36:39Z","cross_cats_sorted":[],"title_canon_sha256":"b7931d2f942256c4524b21fc22de4aa7b3e0756d74c51ec83714cf23a5c9cec2","abstract_canon_sha256":"0a9923d2e00e4671ed31a9d832584967c5089d92c8e692600bf82e1e5dbbbae7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:03.495835Z","signature_b64":"OD0DTBhIASWO5Pu++o06LQ7WiSD917FguSlY7hbW3ItcSn3RzD0/8W65X7sXJCm0u9Vscr7UetTxHuijzWBEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08735690f184281f7279259dde050ce572def259976b3f961c2e52d53bd43682","last_reissued_at":"2026-05-18T00:36:03.495289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:03.495289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations associated to small nilpotent orbits for complex 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":"2017-02-27T10:36:39Z","abstract_excerpt":"This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. 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