Pith Number

pith:P2NPIJXP

pith:2026:P2NPIJXPH2IH6GAWZYTIK3BBSZ

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Representation Category of Free Wreath Product of Classical Groups

Yigang Qiu

A rigid concrete C*-tensor category reconstructs the free wreath product of classical groups via Woronowicz-Tannaka-Krein duality.

arxiv:2604.02571 v3 · 2026-04-02 · math.QA

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\usepackage{pith}
\pithnumber{P2NPIJXPH2IH6GAWZYTIK3BBSZ}

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Record completeness

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4 Citations open

5 Replications open

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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

We construct a rigid concrete C*-tensor category whose associated compact quantum group, reconstructed via Woronowicz--Tannaka--Krein duality, is the free wreath product of classical groups.

C2weakest assumption

The constructed category is rigid, concrete, and satisfies all hypotheses of the Woronowicz-Tannaka-Krein duality theorem so that the reconstructed object is exactly the free wreath product.

C3one line summary

A rigid concrete C*-tensor category is built whose Woronowicz-Tannaka-Krein dual is the free wreath product of classical groups.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:30.702097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e9af426ef3e907f1816ce26856c21964fd5250b241bdbd520be8a5a7dc9d24c

Aliases

arxiv: 2604.02571 · arxiv_version: 2604.02571v3 · doi: 10.48550/arxiv.2604.02571 · pith_short_12: P2NPIJXPH2IH · pith_short_16: P2NPIJXPH2IH6GAW · pith_short_8: P2NPIJXP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/P2NPIJXPH2IH6GAWZYTIK3BBSZ \
  | 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: 7e9af426ef3e907f1816ce26856c21964fd5250b241bdbd520be8a5a7dc9d24c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63099b86ecc8298f74e6dbab6f11232811d769ddef0ba15d87580fd10be351a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-04-02T22:51:30Z",
    "title_canon_sha256": "b7910c17f25b99c84f6e258d6605f8f8a9c03e912300c027bbd05fbc8a0bf849"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.02571",
    "kind": "arxiv",
    "version": 3
  }
}