Pith Number

pith:CKAL7FYY

pith:2024:CKAL7FYY63OFKOK7WJKUF2A5GH

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Monoidal Jantzen filtrations

David Hernandez, Ryo Fujita

A monoidal Jantzen filtration deforms the Grothendieck ring multiplication into an associative quantization that matches the geometric version for simply-laced quantum loop algebras.

arxiv:2402.13544 v5 · 2024-02-21 · math.RT · math.QA

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Claims

C1strongest claim

The monoidal Jantzen filtration induces a deformation of the multiplication on the Grothendieck ring that is associative for finite-dimensional representations of simply-laced quantum loop algebras, and the resulting quantization coincides with the quantum Grothendieck ring of Nakajima and Varagnolo-Vasserot.

C2weakest assumption

The monoidal abelian category admits a generic braiding and satisfies the technical conditions needed for the Jantzen filtration to be well-defined and to induce a deformation whose associativity can be checked via explicit computations in the cited representation categories.

C3one line summary

Monoidal Jantzen filtrations induce an associative deformation of Grothendieck ring multiplication that quantizes the ring and recovers known quantum versions in representation categories of quantum loop algebras and quiver Hecke algebras.

Receipt and verification

First computed	2026-06-09T02:06:59.086025Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1280bf9718f6dc55395fb25542e81d31e59641c10d8d8ff34305e738192eaa5a

Aliases

arxiv: 2402.13544 · arxiv_version: 2402.13544v5 · doi: 10.48550/arxiv.2402.13544 · pith_short_12: CKAL7FYY63OF · pith_short_16: CKAL7FYY63OFKOK7 · pith_short_8: CKAL7FYY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CKAL7FYY63OFKOK7WJKUF2A5GH \
  | 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: 1280bf9718f6dc55395fb25542e81d31e59641c10d8d8ff34305e738192eaa5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab014b521166b04423a6be300f2b72aa6b361f8326f659d295306a276d4fac16",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2024-02-21T05:53:28Z",
    "title_canon_sha256": "4b893d1badbf5a23b8a6e3e79cadb8970ef0e9185407c01196e139ce6254f94d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.13544",
    "kind": "arxiv",
    "version": 5
  }
}