Pith Number

pith:3AZG7IYX

pith:2026:3AZG7IYXEBBS4AAP6QNMLFPD7X

not attested not anchored not stored refs resolved

Quiver varieties and dual canonical bases

Ming Lu, Xiaolong Pan

Dual canonical bases of quantum groups coincide with Berenstein-Greenstein double canonical bases.

arxiv:2605.13578 v1 · 2026-05-13 · math.QA · math.RT

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\usepackage{pith}
\pithnumber{3AZG7IYXEBBS4AAP6QNMLFPD7X}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

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 demonstrate that the dual canonical bases of quantum groups coincide with the double canonical bases defined by Berenstein and Greenstein, and resolve several conjectures therein.

C2weakest assumption

That the i-quiver algebras correctly provide the two realizations of quasi-split i-quantum groups (via i-Hall algebras and quantum Grothendieck rings of the specified quiver varieties) as stated in the prior introduction by Wang and the first author.

C3one line summary

Dual canonical bases of quantum groups coincide with double canonical bases via i-quiver algebra and quiver variety constructions, with new proofs of positivity and braid group invariance.

References

88 extracted · 88 resolved · 0 Pith anchors

[1] Achar, Perverse sheaves and applications to representation theory, vol 2021

[2] M. Auslander and R. Buchweitz,

[3] H. Bao, J. Kujawa, Y. Li and W. Wang,

[4] H. Bao, P. Shan, W. Wang and B. Webster,

[5] H. Bao and W. Wang, A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs , Ast\'erisque 402, 2018, vii+134pp 2018

Receipt and verification

First computed	2026-05-18T02:44:23.264152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8326fa31720432e000ff41ac595e3fdfdc3f29c12b10542199655515fbcd7ee

Aliases

arxiv: 2605.13578 · arxiv_version: 2605.13578v1 · doi: 10.48550/arxiv.2605.13578 · pith_short_12: 3AZG7IYXEBBS · pith_short_16: 3AZG7IYXEBBS4AAP · pith_short_8: 3AZG7IYX

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/3AZG7IYXEBBS4AAP6QNMLFPD7X \
  | 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: d8326fa31720432e000ff41ac595e3fdfdc3f29c12b10542199655515fbcd7ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "071b88e86cd8a561dce3f6327ed533bca03b60bdd06b738356c3947d6160f432",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-13T14:12:30Z",
    "title_canon_sha256": "ee90fea16e2f2d5b5ed0b3526ee413b389cc93c59ce098e97239f74cf151bbf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13578",
    "kind": "arxiv",
    "version": 1
  }
}