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As an application, we use the structure of the based ring to study certain simple modules of Hecke algebras of $ W $ with unequal parameters, namely those attached to $\\mathbf{c}_0$.\n  Also we give a set of prime ideals $\\mathfrak{p}$ of the center $\\mathcal{Z}$ of the generic affine Hecke algebra $\\mathcal{H}$ such that th"},"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":"1403.3213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-13T09:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"99dbcfcd186f7bdfae2a4086ffb750a93413ec3d68456874bc8f88d7f96e4ce8","abstract_canon_sha256":"ae0fed9e28b04b43e0241a9db448d670518565a2bb88cfda485b5a1bb76cbbe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:41.968016Z","signature_b64":"FYv83cXaIh6MIeT5nmaNqHEJvYNf8rx6jINs09tJOWyZn8VrmBb554fxFw2fBZGBeoZFd5A4gx7dM54Ug9QcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d866fa7b9987785bdeea1c131d8e2eca36c89ecfc4d60ad9d8d96e88cf1c8267","last_reissued_at":"2026-05-18T01:32:41.967514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:41.967514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The based ring the lowest generalized two-sided cell of an extended affine Weyl group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Xun Xie","submitted_at":"2014-03-13T09:38:04Z","abstract_excerpt":"Let $\\mathbf{c}_0$ be the lowest generalized two-sided cell of an extended affine Weyl group W. 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