Pith Number

pith:6GS35QCT

pith:2025:6GS35QCTOI5U5CUPX6PN2ZBUVA

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Triality and adjoint lifting for GL(3)

Wee Teck Gan

Cuspidal representations of GL(3) with a discrete series local component lift to automorphic representations on GL(8) by the adjoint map.

arxiv:2512.08307 v3 · 2025-12-09 · math.NT · math.RT

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Using the stable twisted trace formula for the triality automorphism, we show the adjoint lifting (to GL(8)) of cuspidal representations of GL(3) with a discrete series local component.

C2weakest assumption

The cuspidal representations of GL(3) possess at least one discrete series local component, allowing the stable twisted trace formula for triality to apply and produce the global lift.

C3one line summary

Adjoint lifting from cuspidal GL(3) representations to GL(8) is established using the triality automorphism and twisted trace formula, with descriptions of isobaric decompositions and applications to Ramanujan bounds and the strong Artin conjecture.

References

81 extracted · 81 resolved · 0 Pith anchors

[1] M. Asgari and A. Raghuram, A cuspidality criterion for the exterior square transfer of cusp forms on (4) , in On certain L-functions , 33-53, Clay Math. Proc., 13, Amer. Math. Soc., Providence, RI, 20 2011

[2] Arthur, The endoscopic classification of representations: orthogonal and symplectic groups 2013

[3] J. Arthur and L. Clozel, Simple algebras, base change, and the advanced theory of the trace formula , Annals of Mathematics Studies, 120. Princeton University Press, Princeton, NJ, 1989. xiv+230 pp 1989

[4] M. Asgari and F. Shahidi, Generic transfer for general spin groups , Duke Math. J. 132 (2006), no. 1, 137-190 2006

[5] H. Atobe, W.T. Gan, A. Ichino, T. Kaletha, A. Minguez and S.W. Shin, Local intertwining relations and cotempered A-packets of classical groups , arxiv preprint, arXiv:2410.13504

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:32.833639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1a5bec053723b4e8a8fbf9edd6434a8261c0e32cdffa2c9b75329ad05876f07

Aliases

arxiv: 2512.08307 · arxiv_version: 2512.08307v3 · doi: 10.48550/arxiv.2512.08307 · pith_short_12: 6GS35QCTOI5U · pith_short_16: 6GS35QCTOI5U5CUP · pith_short_8: 6GS35QCT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6GS35QCTOI5U5CUPX6PN2ZBUVA \
  | 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: f1a5bec053723b4e8a8fbf9edd6434a8261c0e32cdffa2c9b75329ad05876f07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "792e0855639ab59aafe9ca75a8dd39197c142bbf853110742e9bc5f8724ffe7f",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-12-09T07:09:51Z",
    "title_canon_sha256": "9d424285f7a5a5b6c732f8209f12f7da80dd7b9c8ff3ec2d32821b917ef62f1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.08307",
    "kind": "arxiv",
    "version": 3
  }
}