Pith Number

pith:5RVP6E6R

pith:2026:5RVP6E6RZHFYZSYL55DBOZPIYZ

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Middle convolution for Lie algebra representations

Kazuki Hiroe

A middle convolution functor on Lie algebra modules generalizes several classical constructions and establishes a Riemann-Hilbert correspondence with geometric middle convolution.

arxiv:2605.09828 v2 · 2026-05-11 · math.RT · math.AG

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\pithnumber{5RVP6E6RZHFYZSYL55DBOZPIYZ}

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4 Citations 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 establish a Riemann-Hilbert correspondence between the middle convolution for the holonomy Lie algebra and the middle convolution for local systems on complements of hyperplane arrangements.

C2weakest assumption

That the middle convolution functor can be defined consistently on the category of modules over the listed Lie algebras (free, Drinfeld-Kohno, holonomy) in a way that simultaneously generalizes the infinitesimal Long-Moody functor, recovers Dettweiler-Reiter convolution, and is compatible with Haraoka's construction.

C3one line summary

The paper introduces a Lie algebra analogue of the middle convolution functor and proves it generalizes the Long-Moody functor, recovers Dettweiler-Reiter convolution, is compatible with Haraoka's version, and satisfies a Riemann-Hilbert correspondence for holonomy Lie algebras.

Receipt and verification

First computed	2026-06-09T02:07:28.819257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec6aff13d1c9cb8ccb0bef461765e8c6479bc4d09d8be53ec9f41b5b2fa23a18

Aliases

arxiv: 2605.09828 · arxiv_version: 2605.09828v2 · doi: 10.48550/arxiv.2605.09828 · pith_short_12: 5RVP6E6RZHFY · pith_short_16: 5RVP6E6RZHFYZSYL · pith_short_8: 5RVP6E6R

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5RVP6E6RZHFYZSYL55DBOZPIYZ \
  | 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: ec6aff13d1c9cb8ccb0bef461765e8c6479bc4d09d8be53ec9f41b5b2fa23a18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e528f9366517be990886b0ab91e125cb433844e97b26018a605298a0b48ab93",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-11T00:08:35Z",
    "title_canon_sha256": "6f9bd2a0eb3b6ff4a681a996303150b9a47171c1a37d847b873b32a2d8a9ccf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09828",
    "kind": "arxiv",
    "version": 2
  }
}