{
  "abstract": "Let $G_0$ be a real form of a complex semisimple group acting on a flag manifold $Z$, with maximal compact subgroup $K_0$ and its complexification $K$. Matsuki duality pairs each $G_0$-orbit $γ$ with a $K$-orbit $κ$, and $M=κ\\capγ$ is a compact $K_0$-orbit. For lower-dimensional $γ$, $M$ is a compact CR manifold, and we ask which functions are holomorphic near $M$ and what its holomorphic hull is. In general, we show that $K_0$-finite holomorphic functions near $M$ are regular functions on $K$-orbits, and that $M$ carries non-constant holomorphic germs if some $K$-stable prime divisor of $Z$ misses $κ$, and, under a connectedness hypothesis, only constants otherwise. For $G_0=SU(p,q)$ acting on any Grassmannian $\\mathrm{Gr}_k(\\mathbb{C}^{p+q})$ we give a complete answer. Holomorphic functions near $M$ are constant unless $M$ is of holomorphic type: $k\\in\\{p,q\\}$ and $M$ lies in the Harish-Chandra chart of the bounded symmetric domain $\\mathcal{D}$. Then $M$ is the manifold of rank-$c$ partial isometries, and a holomorphic hull of $M$ is $\\overline{\\mathcal{D}}\\cap\\{\\mathrm{rank}\\le c\\}$. This agrees with the polynomial hull of Kaup and Zaitsev except in one totally real case, where it is strictly smaller because $\\det^{-1}$ is holomorphic near $U(p)$. The same dichotomy decides when global CR functions on $M$ are constant and when holomorphic sections of line bundles near $M$ are global; its exceptions differ from the Gindikin-Matsuki exceptions for cycle spaces, except at the base point of $\\mathcal{D}$. This settles the descent question left open in earlier work with K. Shabbir on rank-one orbits. We also determine which $K$-orbits carry non-constant regular functions, prove constancy via chains of rational curves for small $c$, and compute Levi forms in examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41828",
  "author_total": 1,
  "authors": [
    {
      "name": "Irfan Ullah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zdazgsr54f5n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41828",
  "fulltext_url": null,
  "id": "7zdazgsr54f5n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41828",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zdazgsr54f5n.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Holomorphic functions and hulls of Matsuki-dual orbits of $SU(p,q)$ in complex Grassmannians",
  "title_text": "Holomorphic functions and hulls of Matsuki-dual orbits of SU(p,q) in complex Grassmannians",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/7zdazgsr54f5n",
  "venue": "arXiv",
  "versions": []
}