Pith Number

pith:LFTKWJWK

pith:2026:LFTKWJWKLBVXGGXMGKIRCRDTH5

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Shifted quantum toroidal algebra of type $\mathfrak{gl}_{1|1}$ and the Pieri rule of the super Macdonald polynomials

Hiroaki Kanno, Jun'ichi Shiraishi, Ryo Ohkawa

The action of super charges from the shifted quantum toroidal algebra of type gl_{1|1} implies the Pieri rule for super Macdonald polynomials.

arxiv:2605.16773 v1 · 2026-05-16 · math.QA · hep-th · math-ph · math.MP

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Claims

C1strongest claim

The action of the super charges of U_{q,t}(widehat{widehat{gl}}_{1|1}) implies the Pieri rule of the super Macdonald polynomials.

C2weakest assumption

The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module of the quantum toroidal algebra.

C3one line summary

Super Macdonald polynomials indexed by super partitions form a basis of the level zero super Fock module of the shifted quantum toroidal algebra U_{q,t}(gl hat hat 1|1), with the Pieri rule following from super charge actions and yielding supersymmetric Hamiltonians via anti-commutators.

References

23 extracted · 23 resolved · 9 Pith anchors

[1] Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet) 1903 · arXiv:1903.07777

[2] Quantum Algebraic Approach to Refined Topological Vertex 2012 · arXiv:1112.6074

[3] Collective fields, Calogero-Sutherland model and generalized matrix models 1995 · arXiv:hep-th/9411053

[4] Quantum W(N) algebras and Macdonald polynomials, 1996

[5] Macdonald polynomials in superspace: conjectural definition and positivity conjectures 2012 · arXiv:1112.5188

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:21.225429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5966ab26ca586b731aec32911144733f7823393e184cd6e63a9dcb1ed24e337a

Aliases

arxiv: 2605.16773 · arxiv_version: 2605.16773v1 · doi: 10.48550/arxiv.2605.16773 · pith_short_12: LFTKWJWKLBVX · pith_short_16: LFTKWJWKLBVXGGXM · pith_short_8: LFTKWJWK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LFTKWJWKLBVXGGXMGKIRCRDTH5 \
  | 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: 5966ab26ca586b731aec32911144733f7823393e184cd6e63a9dcb1ed24e337a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d4a3ba3a9a2f1707ffedc1846171b1e0459174c362cc7695e263815719847e",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-16T02:50:52Z",
    "title_canon_sha256": "336c4373eba708a41cad82521e6140bf73b6835e17686d7bd9c5a49c32afa7c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16773",
    "kind": "arxiv",
    "version": 1
  }
}