Pith Number

pith:OFS3NOMF

pith:2026:OFS3NOMFLR2RGULKP6BBLIWYS3

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The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groups

Amoru Fujii

The local Langlands correspondence is constructed for essentially unipotent supercuspidal representations of disconnected reductive groups using rigid inner forms.

arxiv:2604.25198 v2 · 2026-04-28 · math.RT · math.NT

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Claims

C1strongest claim

We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certain functoriality and compatibilities. In particular, we show the equivariance under automorphisms, which is stronger than the analogous result in [FOS20]. We also generalize this correspondence for disconnected reductive groups under a mild condition on the group structure.

C2weakest assumption

The generalization to disconnected reductive groups holds under a mild condition on the group structure, and the entire construction relies on the framework of rigid inner forms.

C3one line summary

Constructs local Langlands correspondence for essentially unipotent supercuspidal representations with functoriality and automorphism equivariance, generalizing to disconnected reductive groups under a mild structural condition.

Receipt and verification

First computed	2026-05-20T01:05:14.435231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7165b6b9855c7513516a7f8215a2d896faeebf4c1c9dead9b2ddf2c4d3832f67

Aliases

arxiv: 2604.25198 · arxiv_version: 2604.25198v2 · doi: 10.48550/arxiv.2604.25198 · pith_short_12: OFS3NOMFLR2R · pith_short_16: OFS3NOMFLR2RGULK · pith_short_8: OFS3NOMF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OFS3NOMFLR2RGULKP6BBLIWYS3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7165b6b9855c7513516a7f8215a2d896faeebf4c1c9dead9b2ddf2c4d3832f67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccf9b5853f6088c48a94bd736733bf1353cac8d738e5131fcaf005cfcf4c6e2c",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-04-28T04:08:18Z",
    "title_canon_sha256": "26bf105c6760c24cbc3b5aad5ca7db39cb52b35398cc8f9b43093cd828fb1f0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25198",
    "kind": "arxiv",
    "version": 2
  }
}