{
  "abstract": "We classify the reduced decompositions of the longest element $w_0$ of the Weyl group of a semisimple Lie algebra $\\mathfrak{g}$ for which the corresponding Lusztig quantum root vectors span a quantum tangent space in $U_q(\\mathfrak{g})$. We introduce a combinatorial condition on the convex order induced by a reduced decomposition, tangency, and prove that a reduced decomposition gives rise to a quantum tangent space if and only if it is tangent. The proof relies on a description of the coproduct of quantum root vectors in terms of the convex order, and on a projection in the right weak order attached to each positive root. Up to commutation, tangent reduced decompositions are obtained by concatenating the longest minimal coset representatives along a chain of cominuscule parabolic quotients; in particular there are none in types $E_8$, $F_4$ and $G_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35091",
  "author_total": 3,
  "authors": [
    {
      "name": "Alessandro Carotenuto"
    },
    {
      "name": "Christophe Hohlweg"
    },
    {
      "name": "Paolo Papi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bhx765fa617mm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35091",
  "fulltext_url": null,
  "id": "bhx765fa617mm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35091",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223883232",
  "pdf_url": "https://arxiv.org/pdf/2610.35091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bhx765fa617mm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Convex orders in root systems and quantum tangent spaces",
  "title_text": "Convex orders in root systems and quantum tangent spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bhx765fa617mm",
  "venue": "arXiv",
  "versions": []
}