{
  "abstract": "Crystal bases are powerful combinatorial tools in the representation theory of quantum groups U q ( 𝔤 ) for a symmetrizable Kac-Moody algebras 𝔤 . The polyhedral realizations are combinatorial descriptions of the crystal base B ( ∞ ) for Verma modules in terms of the set of integer points of a polyhedral cone, which equals the string cone when 𝔤 is finite dimensional simple. It is a fundamental and natural problem to find explicit forms of the polyhedral cone. The monomial realization expresses crystal bases B ( λ ) of integrable highest weight representations as Laurent monomials with double indexed variables. In this paper, we give a conjecture between explicit forms of the polyhedral cones and monomial realizations. We prove the conjecture is true when 𝔤 is a classical Lie algebra, a rank 2 Kac-Moody algebra or a nonexceptional affine Lie algebra.",
  "abstract_shown": true,
  "affiliations": [
    "Ibaraki University, Faculty of Basic Natural Science, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512 (Japan)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yuki Kanakubo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xfw6mj8y31s8.bib",
  "cited_by": 0,
  "doi": "10.5802/alco.518",
  "fulltext_url": null,
  "id": "1xfw6mj8y31s8",
  "issns": [
    "2589-5486"
  ],
  "landing_url": "https://alco.centre-mersenne.org/articles/10.5802/alco.518/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W4414564949",
  "pdf_url": "https://alco.centre-mersenne.org/item/10.5802/alco.518.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "MathDoc/Centre Mersenne",
  "ris": "https://research.draconitic.com/paper/1xfw6mj8y31s8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:25Z",
      "native_id": "10.5802/alco.518",
      "source": "crossref",
      "url": "https://alco.centre-mersenne.org/articles/10.5802/alco.518/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A conjecture on monomial realizations and polyhedral realizations for crystal bases",
  "title_text": "A conjecture on monomial realizations and polyhedral realizations for crystal bases",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:25Z",
  "url": "https://research.draconitic.com/paper/1xfw6mj8y31s8",
  "venue": "Algebraic Combinatorics",
  "versions": []
}