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Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian conformal structures, namely $SO_0(2,n)$, SU(1,n), and $SO_0(1,2)$."},"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":"0806.2586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-06-16T14:06:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dde86fbb861d03fa3a0ce556530dff78ae1dab681141e63d3895e9d26eb164e4","abstract_canon_sha256":"38db0bfabc62d6163d469df97c3fab1f2c43f55168522a08165ff8ab7f8a2ecd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:59.462250Z","signature_b64":"lnC2af/G/fdoOPa+gi9ArV8s+S+KrG1zWzAapqIMe5clNdptGIoM84pYagt3t52nZ8iB+BALl6I8yfQmI3SFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d0640ab072a3fd74def4579e2af17099b9e2d6f0fcc8eaaca2127491d8263b0","last_reissued_at":"2026-05-18T03:48:59.461708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:59.461708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connected subgroups of SO(2,n) acting irreducibly on $\\R^{2,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"Antonio J. Di Scala, Thomas Leistner","submitted_at":"2008-06-16T14:06:37Z","abstract_excerpt":"We classify all connected subgroups of SO(2,n) that act irreducibly on $\\R^{2,n}$. Apart from $SO_0(2,n)$ itself these are $U(1,n/2)$, $SU(1,n/2)$, if $n$ even, $S^1\\cdot SO(1,n/2)$ if $n$ even and $n\\ge 2$, and $SO_0(1,2)$ for $n=3$. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. 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