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We prove that the dimension of the tensor invariant space of G_{\\sigma} is equal to the trace of {\\sigma} on the corresponding tensor invariant space of G. We prove that if G has the saturation property then so does G{\\sigma}. As a consequence, we show that the spin group Spin(2n + 1) is of saturation property with factor 2, which strengthens the results of Belkale-Kumar and Sam in the case of type B_n."},"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":"1404.4098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-15T22:19:06Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"158e8f7f446b9f663918b904795c0d874840b96e92e67325bc9d796dc0a7e131","abstract_canon_sha256":"2fdb49a8af5d8e32548496ea30599755bfa45a5a6e92bc83a5f7047bb53b4e6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:21.248207Z","signature_b64":"BMent1ljnTrSeaCjEPwYoEfRXACgtkes/I9oAXD5+XiLDxIs1yN1dmfqWTvxPJsCz8JbKgwjNnqxUoBQGkv5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f7c27b03d3136f22eeefe713b2b85e237745d613b441ee165ec13a3e985dca0","last_reissued_at":"2026-05-17T23:40:21.247606Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:21.247606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor invariants, Saturation problems, and Dynkin automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Jiuzu Hong, Linhui Shen","submitted_at":"2014-04-15T22:19:06Z","abstract_excerpt":"Let G be a connected almost simple algebraic group with a Dynkin automorphism {\\sigma}. 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