Pith Number

pith:JTBRITYN

pith:2025:JTBRITYNC3KPUZKJ3GOGYWN3CR

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A Nakayama result for the quantum K theory of homogeneous spaces

Eric Sharpe, Hao Zhang, Hao Zou, Leonardo C. Mihalcea, Wei Gu, Weihong Xu

The ideal of relations in the quantum K ring of a homogeneous space is generated by quantizations of the classical generators.

arxiv:2507.15183 v2 · 2025-07-21 · math.AG · math.CO

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Claims

C1strongest claim

We prove that the ideal of relations in the (equivariant) quantum K ring of a homogeneous space is generated by quantizations of each of the generators of the ideal in the classical (equivariant) K ring.

C2weakest assumption

The quantum K-ring is constructed so that its ideal of relations is generated precisely by the images of the quantized classical generators under the natural map from the classical ring (abstract, page 1).

C3one line summary

Proves that the ideal of relations in the equivariant quantum K-ring of homogeneous spaces is generated by quantizations of the classical K-ring generators, extending Siebert-Tian.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] [Eis95] David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol 2009

[2] MR1786492 (2001m:14078) [GK17] Vassily Gorbounov and Christian Korff, Quantum integrability and generalised quantum Schubert cal- culus, Adv 2017

[3] MR4719974 14 WEI GU, LEONARDO C. MIHALCEA, ERIC SHARPE, WEIHONG XU, HAO ZHANG, AND HAO ZOU Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou, Zhejiang 310058, Chin

Formal links

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Cited by

3 papers in Pith

Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries

Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

Receipt and verification

First computed	2026-05-20T14:03:19.735563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cc3144f0d16d4fa6549d99c6c59bb1465469ec8a4dbaa26b98158115c1f3545

Aliases

arxiv: 2507.15183 · arxiv_version: 2507.15183v2 · doi: 10.48550/arxiv.2507.15183 · pith_short_12: JTBRITYNC3KP · pith_short_16: JTBRITYNC3KPUZKJ · pith_short_8: JTBRITYN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JTBRITYNC3KPUZKJ3GOGYWN3CR \
  | 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: 4cc3144f0d16d4fa6549d99c6c59bb1465469ec8a4dbaa26b98158115c1f3545

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c3681e02c3a8422e75154434fe373bd739ce52ca3f76ca0e71d17619b7c70f8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-21T02:03:53Z",
    "title_canon_sha256": "cb0524b4cc891d41aa49975cfba73983614f1c0fb1ecc586e04939dfc76a9fe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15183",
    "kind": "arxiv",
    "version": 2
  }
}