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In this paper we construct an associated degeneration of homogeneous coordinate rings of classical flag varieties in all types and show that these rings are Frobenius split in most types. It follows that the degenerate flag varieties of types $A_n$, $C_n$ and $G_2$ are Frobenius split. In particular we obtain an altern"},"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":"1307.7634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-29T16:26:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"8cdba6e4ac763607345a181ab97564231340385bc94c91e863bd05a1ea98cd63","abstract_canon_sha256":"6babe0186504701d8f103b59c99070ebd028a4904d66e03913d1354885779da4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:08.355584Z","signature_b64":"dp6DrN3q38JE7whVCU+Fo+1uQLWp/obloA70jj2AqLHlMG86AUzycRSb/UhBNCmZ297UyYAZ1/3nvPKPWTRKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f6d6a4e873eb67d9118e2239c0ac7e78fcb82b6cd61ad2a0c39a2888f6a592","last_reissued_at":"2026-05-18T03:16:08.354886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:08.354886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degenerate coordinate rings of flag varieties and Frobenius splitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Chuck Hague","submitted_at":"2013-07-29T16:26:40Z","abstract_excerpt":"Recently E. Feigin introduced the $\\mathbb G_a^N$-degenerations of semisimple algebraic groups and their associated degenerate flag varieties. It has been shown by Feigin, Finkelberg, and Littelmann that the degenerate flag varieties in types $A_n$ and $C_n$ are Frobenius split. In this paper we construct an associated degeneration of homogeneous coordinate rings of classical flag varieties in all types and show that these rings are Frobenius split in most types. It follows that the degenerate flag varieties of types $A_n$, $C_n$ and $G_2$ are Frobenius split. 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