{
  "annotation_id": "22d2e5f9-9036-40bd-b3e4-395d893e4110",
  "date_created": "2026-02-17T05:53:04.191000Z",
  "date_modified": "2026-02-17T05:53:04.191000Z",
  "file_hash": "0b2f361cb0ae235b6b6985b04361b1b5d89bcd4dcab664cc2e7871d41e9805d7",
  "private": false,
  "record": {
    "abstract": "This article introduces a framework for the localization and isolation of singularities in the affine Grassmannian. Our primary result is a structural factorization of the transition matrix $C$ between the Mirkovi\\\u0027c--Vilonen (MV) basis and the convolution basis into $C = P \\cdot M \\cdot A \\cdot Q^{-1}$, where the four factors represent: equivariant localization ($Q$), fusion via nearby cycles ($A$), local intersection cohomology stalks ($M$), and diagonal normalization ($P$). Utilizing this factorization, and by introducing the Geometric Efficiency metric ($\\eta$) we establish a Universal Geometric Rank Bound, proving that the rank of the transition matrix $C$ is bounded by the dimension of the local Braden--MacPherson (BMP) stalks.",
    "arxiv_id": "2601.05369",
    "authors": [
      "George Petroulakis"
    ],
    "categories": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Localization of Singularities and Universal Geometric Rank Bounds in the Satake Correspondence",
    "url": "https://arxiv.org/abs/2601.05369",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2af8edfc-66f5-42e6-aef9-58fb5f4dd9f7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}