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We find that the restriction of an \\check{\\mathscr{H}}_{r,2}-irreducible to \\check{\\mathscr{H}}_{r-1,2} is multiplicity-free, and as a consequence, any \\check{\\mathscr{H}}_{r,2}-irreducible has a seminormal basis "},"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":"1201.2209","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-10T23:55:01Z","cross_cats_sorted":[],"title_canon_sha256":"e3a52c5b2b0955dc3bb15ecbe5f1bc57a02794be232e8b686ccb203c523b2c2d","abstract_canon_sha256":"e7fa86756e63bcb2053981b88e7ddf0a7eb4977b5f79c84d083a61732b10e7ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:06.308060Z","signature_b64":"sOiHAeEGVH22KRQwnAuHNIaeLVHTNKHixcrRaZMx6t/ciPiwyjC3JgZxVSKBqXMZrFvokl4b5LuOMh7ReSRrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec03a5ea31b4d2986db8681238418801fa0597c97ea7efb02e4d422e56a4b68","last_reissued_at":"2026-05-18T04:03:06.307299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:06.307299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representation theory of the nonstandard Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonah Blasiak","submitted_at":"2012-01-10T23:55:01Z","abstract_excerpt":"The nonstandard Hecke algebra \\check{\\mathscr{H}}_r was defined by Mulmuley and Sohoni to study the Kronecker problem. 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