{
  "abstract": "Let $Q$ be a bipartite Dynkin quiver of finite simply-laced type and $\\mathscr C_Q$ the corresponding Hernandez--Leclerc category. We study a two-parameter specialization of the Fedele--Hernandez toroidal Grothendieck ring and identify its generic positive part with a Cartan-type multiparameter quantum group. The structural input is the identity \\[ 2D^{(2)}-D_0=ω_Q\\circ(°_Q,°_Q), \\] where $D_0,D^{(2)}$ are the two effective toroidal commutation forms and $ω_Q$ is the antisymmetric Euler form of \\(Q\\). It realizes the specialized character algebra, after an auxiliary scalar extension, as a graded bicharacter twist of the one-parameter algebra at $v=t_0t^{1/2}$. This yields the required root grading and PBW graded dimensions. For every source--sink edge $r\\to s$, these dimensions combine with the local \\(A\\)--\\(Y\\) commutation formula to give a quadratic annihilator for \\(\\operatorname{Ad}_{Z_r}\\). Consequently \\[ \\operatorname{Spec}_{Z_r}(Z_s)=\\{t_0t,t_0^{-1}\\}, \\] without thinness or type-specific character formulas. The two spectral values yield the oriented multiparameter Serre relations. With \\[ q_{ii}=t_0^2t,\\qquad q_{ij}=t_0^{-1},\\qquad q_{ji}=t_0^{-1}t^{-1}\\quad(i\\to j), \\] and \\(q_{ij}=1\\) on nonedges, we obtain \\[ U_{\\mathbf q}^{+}(\\mathfrak g) \\simeq \\mathscr K_\\infty(\\mathscr C_Q)\\otimes_RK \\] for $\\mathfrak g$ of type $A_n,D_n,E_6,E_7,E_8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04189",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaomin Tang"
    },
    {
      "name": "Yu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cakb8rpj3hz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04189",
  "fulltext_url": null,
  "id": "1cakb8rpj3hz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04189",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220663803",
  "pdf_url": "https://arxiv.org/pdf/2610.04189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cakb8rpj3hz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04189"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Spectral Rigidity in Toroidal Grothendieck Rings and Multiparameter Quantum Groups",
  "title_text": "Spectral Rigidity in Toroidal Grothendieck Rings and Multiparameter Quantum Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1cakb8rpj3hz5",
  "venue": "arXiv",
  "versions": []
}