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Also, the $L$-packet $\\Pi(\\varphi_{\\lambda})$ associated to $\\lambda$ is parametrized by an abelian group $\\hat{R}$. We show that $\\hat{R}$ is naturally a homogenous space for $\\hat{\\Omega}$. Further, le"},"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":"1212.1439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-06T20:25:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"75a20769eaef84034f3bb73096fdd75f5f996727e75dcfdd17424fdbe3feb896","abstract_canon_sha256":"fcf6f4ee4c4fa92611261e30d5b7ea1911eeddc361b7cd19dfc6795e083ce61e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:47.436930Z","signature_b64":"31Ld8kv5v+/vU9J85CVpdJwPq6piJOXrHb59OGogykL1YzLVLY4JkvQuny5qiEij9KZvEjQN2z930PZDAQUeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f5c7791643fd4e6ca3f42c4f2fb4e93822470555a5a2b6cb8d6ed75185209b4","last_reissued_at":"2026-05-18T03:08:47.436099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:47.436099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of the Unramified L-packet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Manish Mishra","submitted_at":"2012-12-06T20:25:32Z","abstract_excerpt":"Let $\\boldsymbol{G}$ be an unramified connected reductive group defined over a non-archemedian local field $k$ and let $\\boldsymbol{T}$ be a maximal torus in $\\boldsymbol{G}.$ Let $\\lambda$ be an unramified character of $\\boldsymbol{T}.$ Then the conjugacy classes of hyperspecial subgroups of $\\boldsymbol{G}(k)$ is a principal homogenous space for a certain finite abelian group $\\hat{\\Omega}$. Also, the $L$-packet $\\Pi(\\varphi_{\\lambda})$ associated to $\\lambda$ is parametrized by an abelian group $\\hat{R}$. We show that $\\hat{R}$ is naturally a homogenous space for $\\hat{\\Omega}$. 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