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Let $W$ denote the Weyl group of $\\mathbf{G}$, namely the symmetric group $\\mathfrak{S}_n$. We elucidate the structure of the extended quotient $\\mathbf{S}_k // W$ as an algebraic variety and of $T_k // W$ as a topological space, in both cases describing them as bundles over unions of tori. Corresponding to the invariance of $K$-theory under Langlands duality, this ca"},"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":"1611.05218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-11-16T10:54:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"b755ecfaa07439008c28757463e0f4dd68fccbc50c7a47b5304cb851bd85c268","abstract_canon_sha256":"5ba3845f1190969f1083cd1b67c1769d4a9019f238cc5923ab6e6b2ae0a99861"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:27.632942Z","signature_b64":"OHVMl6pwaOTtJDyOV8OdCodp09aIutoEdGmfXPgIZoqlAMwAfY+3c2R2BR1NIPu+BUsbuCo28OZMFUqiehT3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8144acc1b62407bafeb640dedcba6875f6959b136e315cac1b1e410f74ad4000","last_reissued_at":"2026-05-18T00:58:27.631932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:27.631932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stratified Langlands duality in the $A_n$ tower","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.KT","authors_text":"Graham A. Niblo, Nick Wright, Roger Plymen","submitted_at":"2016-11-16T10:54:58Z","abstract_excerpt":"Let $\\mathbf{S}_k$ denote a maximal torus in the complex Lie group $\\mathbf{G} = \\mathrm{SL}_n(\\mathbb{C})/C_k$ and let $T_k$ denote a maximal torus in its compact real form $\\mathrm{SU}_n(\\mathbb{C})/C_k$, where $k$ divides $n$. Let $W$ denote the Weyl group of $\\mathbf{G}$, namely the symmetric group $\\mathfrak{S}_n$. We elucidate the structure of the extended quotient $\\mathbf{S}_k // W$ as an algebraic variety and of $T_k // W$ as a topological space, in both cases describing them as bundles over unions of tori. 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