{
  "abstract": "In this paper, we show that the domain $\\mathbb H$ serves as a unifying domain for $\\mathbb G_2, \\mathbb E$ and $\\mathbb P$ by proving that each of these domains is an analytic retract of $\\mathbb H$. Further, we prove that the bidisc $\\mathbb D^2$ and the Euclidean unit ball $\\mathbb B_2$ are also analytic retracts of $\\mathbb H$. Then the rational $\\overline{\\mathbb H}$-inner functions, i.e., the rational maps from $\\mathbb D$ into $\\overline{\\mathbb H}$ whose boundary values lie in the distinguished boundary of $\\mathbb H$, are characterized. Two different versions of Schwarz type lemma for $\\mathbb H$ are established of which one provides a necessary and sufficient condition. Finally, capitalizing on the theory of $\\mathbb H$, we present alternative proofs to a few known results on $\\mathbb P$ from the literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38677",
  "author_total": 3,
  "authors": [
    {
      "name": "Indranil Biswas"
    },
    {
      "name": "Sourav Pal"
    },
    {
      "name": "Nitin Tomar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3st408gnhf77s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38677",
  "fulltext_url": null,
  "id": "3st408gnhf77s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38677",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38677",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3st408gnhf77s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38677",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38677"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On a family of domains associated with $μ$-synthesis in $M_2(\\mathbb C)$",
  "title_text": "On a family of domains associated with μ-synthesis in M_2(ℂ)",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3st408gnhf77s",
  "venue": "arXiv",
  "versions": []
}