{
  "annotation_id": "822222c5-fd30-43d1-b9a9-3abe6a352e3a",
  "date_created": "2026-02-17T05:53:15.943000Z",
  "date_modified": "2026-02-17T05:53:15.943000Z",
  "file_hash": "81b9d050f43fb5ea875216e7dd53b4217ae6a046ec05ef378ef4f732f7ba4e5c",
  "private": false,
  "record": {
    "abstract": "The McKay correspondence establishes a bijection between the cohomology of a minimal resolution and the irreducible representations of a finite subgroup $\\Gamma \\subset \\text{SU}(2)$. While traditional proofs rely on static algebraic isomorphisms, we propose a dynamical framework grounded in gauge theory and Morse-Bott theory. We analyze an $S^1$-invariant Morse-Bott function on the minimal resolution, interpreting its gradient flow lines as $1$-parameter families of holonomy representations of flat connections from $\\Gamma$ to $GL(R)$. We conjecture that the flow emanating from a critical submanifold converges asymptotically at the boundary to a specific irreducible representation of $\\Gamma$. This dynamical process explicitly constructs the identification between the cohomology basis and the irreducible representations of $\\Gamma$ prescribed by the McKay correspondence. We prove this conjecture for cyclic cases.",
    "arxiv_id": "2601.08195",
    "authors": [
      "Jiajun Yan"
    ],
    "categories": [
      "math.DG",
      "math.GT",
      "math.RT",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A Dynamical Framework for the McKay Correspondence via Gauge-Theoretic Morse Flow",
    "url": "https://arxiv.org/abs/2601.08195",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6b3779a9-f922-4b02-8d01-a11635ab6d01",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}