{
  "abstract": "For a $d$-dimensional vector space $V$ over a field of characteristic zero, we show that $GL(V)$-stable ideals of the universal enveloping algebra of the free two-step nilpotent Lie algebra $\\mathfrak n_2(V)$ are in natural correspondence with filters in Young's lattice of integer partitions with at most $d$ rows. The same classification holds for $GL(V)$-stable Poisson ideals of $S(V\\oplusΛ^2(V))$ with its natural Poisson bracket. As applications, we determine all weak polynomial identities of the $n$-th Weyl algebra relative to its standard generating subspace and of the universal enveloping algebra of the $(2n+1)$-dimensional Heisenberg Lie algebra relative to the Lie algebra itself.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36638",
  "author_total": 2,
  "authors": [
    {
      "name": "Vladimir Dotsenko"
    },
    {
      "name": "Artem Lopatin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aepbka3npy0c6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36638",
  "fulltext_url": null,
  "id": "aepbka3npy0c6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36638",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7224105559",
  "pdf_url": "https://arxiv.org/pdf/2610.36638",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aepbka3npy0c6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36638",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36638"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Young's lattice, invariant ideals, and weak identities",
  "title_text": "Young's lattice, invariant ideals, and weak identities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/aepbka3npy0c6",
  "venue": "arXiv",
  "versions": []
}