{
  "abstract": "Let $G=\\mathrm{SL}_n(\\mathbf C)$ and let $P\\subset G$ be a standard parabolic subgroup with Levi factor $L$. For a $G$-dominant weight $λ$, consider the vector bundle on $T^*(G/P)$ obtained by pulling back the vector bundle on $G/P$ associated to the irreducible $L$-module $V_L(λ)^*$. We express its cohomology as a direct limit of the cohomology of certain line bundles on a Bott--Samelson variety associated to an affine Kac-Moody group. This comparison yields vanishing of higher cohomology and shows that the global sections are generated over $\\mathbf C[\\mathfrak g^*]$ by their degree-zero part $V_G(λ)^*$. Using these results together with the Braverman--Kazhdan intertwiners constructed in earlier joint work with A. Slipper, we give an explicit generating set for $\\mathbf C[T^*(\\mathrm{SL}_n/[P,P])]$. Finally, in an appendix joint with Tom Gannon, we combine these results to show the affinization $\\mathrm{Spec}(\\mathbf{C}[T^*(SL_n/[P,P])])$ has terminal singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04670",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikolay Grantcharov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/652y3sf8p08e2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04670",
  "fulltext_url": null,
  "id": "652y3sf8p08e2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04670",
  "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.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7211901719",
  "pdf_url": "https://arxiv.org/pdf/2609.04670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/652y3sf8p08e2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A",
  "title_text": "Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/652y3sf8p08e2",
  "venue": "arXiv",
  "versions": []
}