{
  "abstract": "This paper explores the algebraic invariants and ergodic behavior of the finite-index inclusions forming commuting squares of $\\text{II}_1$ factors. We begin by establishing how regularity, intermediate-subfactor lattices, and Weyl groups transfer across the commuting square under relative commutant and irreducibility conditions. Furthermore, we provide a complete characterization, via a novel factorization theorem, of the unitary normalizers of the upper inclusion when the lower inclusion is regular. Applying these findings to crossed-product inclusions induced by discrete groups, we introduce a relative eigenbasis property that preserves regular inclusions. Finally, we contrast this by proving that a relative weak mixing condition on the group action forces the crossed-product inclusion to be singular.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23125",
  "author_total": 2,
  "authors": [
    {
      "name": "Keshab Chandra Bakshi"
    },
    {
      "name": "C. Silambarasan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9hf7hzhaqrs1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23125",
  "fulltext_url": null,
  "id": "e9hf7hzhaqrs1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23125",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7204195837",
  "pdf_url": "https://arxiv.org/pdf/2608.23125",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9hf7hzhaqrs1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.23125",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23125"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Structural and Dynamical Properties of Subfactor Commuting Squares",
  "title_text": "Structural and Dynamical Properties of Subfactor Commuting Squares",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/e9hf7hzhaqrs1",
  "venue": "arXiv",
  "versions": []
}