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It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for $SL_n (F)$ enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of $SL_n (F)$. An analogous result is shown in the archimedean case.\n  To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this "},"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":"1305.2638","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-12T21:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"a809d29d69e787e5436dd411405d5c6d2cdd38d3861a5da7a33cd3ee513fe01f","abstract_canon_sha256":"0eca976141de36cecc3d5304343bb0bf380f0ed91b6d8bce5759276bcd4ee4a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:34.651136Z","signature_b64":"/G28gshyYlSxrHHdiiBq0+rulutDi+ABPEQ7rYjwzd+3PmVJ4f9Y1sl4X+q+ol5iEghdy7zblsEdn9NUF8iPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13760feef12ad7d094d5075391b7349b7dfa8cdb96c24c13836d10f7760d2318","last_reissued_at":"2026-05-18T00:55:34.650704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:34.650704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The local Langlands correspondence for inner forms of $SL_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anne-Marie Aubert, Maarten Solleveld, Paul Baum, Roger Plymen","submitted_at":"2013-05-12T21:43:02Z","abstract_excerpt":"Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for $SL_n (F)$ enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of $SL_n (F)$. An analogous result is shown in the archimedean case.\n  To settle the case where F has positive characteristic, we employ the method of close fields. 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