{
  "abstract": "Let $G$ be a compact connected semisimple Lie group, and let $π:G\\to U(V_λ)$ be a finite-dimensional irreducible unitary representation associated with the highest weight $λ$. We prove that coherent projectors are the unique minimizers of the Wehrl entropy over all density matrices on $V_λ$. Similar extremal properties hold for power functions in place of the entropy function. The proof uses a second variation at the extremizer by perturbation in directions associated with Killing fields, similar to the strategy of Frank and Lieb used in \\cite{FrankLieb}. Then the problem reduces to the uncertainty principle characterizing coherent states. This solves the Wehrl-type entropy problem for arbitrary compact connected semisimple Lie groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18919",
  "author_total": 1,
  "authors": [
    {
      "name": "Haonan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8x5kcpscg7fh3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18919",
  "fulltext_url": null,
  "id": "8x5kcpscg7fh3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18919",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.FA"
    ],
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.RT"
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      "3107|Quantum Mechanics and Applications"
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  "openalex": "W7213510777",
  "pdf_url": "https://arxiv.org/pdf/2609.18919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8x5kcpscg7fh3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2609.18919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Wehrl-type entropy problem for compact connected semisimple Lie groups",
  "title_text": "Wehrl-type entropy problem for compact connected semisimple Lie groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8x5kcpscg7fh3",
  "venue": "arXiv",
  "versions": []
}