{
  "abstract": "The loop mirror Heisenberg-Virasoro algebra, an embedded subalgebra of the loop Heisenberg-Virasoro algebra, admits a family of interesting truncated subalgebras including those of Takiff type and \\(\\mathfrak{bms}_3\\) type. We give a complete classification of simple Harish-Chandra modules over the loop mirror Heisenberg-Virasoro algebra, whose simple modules fall into three categories, highest weight modules, lowest weight modules, and evaluation modules of the intermediate series. As a by-product, we classify all simple Harish-Chandra modules over the truncated mirror Heisenberg-Virasoro algebras \\(\\mathcal{L}(n)\\) for \\(n\\geq2\\). By virtue of shift operators in the \\(d\\)-parameter family, we give a more streamlined proof of Theorem 3.3 from the work [Classification of simple $W_n$-modules with finite-dimensional weight spaces, {\\it J. Reine Angew. Math.}, {\\bf 720} (2016), 199-216] by Y. Billig and V. Futorny, which states the key Billig-Futorny identity. Furthermore, our approach can be extended to the computation of annihilators for uniformly bounded modules over some other Lie (super)algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30187",
  "author_total": 3,
  "authors": [
    {
      "name": "Haibo Chen"
    },
    {
      "name": "Xiansheng Dai"
    },
    {
      "name": "Yucai Su"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bfpm5cdev12s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30187",
  "fulltext_url": null,
  "id": "4bfpm5cdev12s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30187",
  "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.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7204878500",
  "pdf_url": "https://arxiv.org/pdf/2608.30187",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bfpm5cdev12s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30187",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30187"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of Simple Harish-Chandra Modules over the Loop Mirror HeisenbergVirasoro Algebra",
  "title_text": "Classification of Simple Harish-Chandra Modules over the Loop Mirror HeisenbergVirasoro Algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/4bfpm5cdev12s",
  "venue": "arXiv",
  "versions": []
}