{
  "abstract": "Let G be a non-trivial finite subgroup of SL_2(C) and let p : X \\to C^2/G be the minimal resolution. We prove the C^*-equivariant Cohomological Crepant Resolution Conjecture for the ADE orbifold [C^2/G]. More precisely, after specializing the quantum parameters at suitable roots of unity, we prove that the Bryan-Gholampour transformation induces an isomorphism between the C^*-equivariant quantum cohomology of X and the C^*-equivariant Chen-Ruan cohomology of [C^2/G]. Our proof is direct and is based on the McKay correspondence, ADE root systems, and character theory. Following the character-theoretic form of the Bryan-Gholampour change of variables, we use the McKay correspondence to diagonalize the transformation and to reduce the compatibility of the products to a uniform root-system identity. In type A, this reduction admits a discrete Fourier realization. In type D, the cyclic subgroup of the binary dihedral group leads instead to finite sine transforms, while the exceptional cases E_6,E_7,E_8 are treated by exact matrix computations over the corresponding cyclotomic fields. As a preliminary result, for a symplectic complex vector space V and a finite subgroup G of Sp(V), we give an explicit presentation of the C^*-equivariant Chen-Ruan product of [V/G] and identify the resulting algebra with the Rees algebra of the center of the group algebra with respect to the age filtration. In particular, the equivariant Chen-Ruan algebra interpolates between the center of the group algebra and its associated graded algebra, the latter recovering the ordinary Chen-Ruan cohomology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17494",
  "author_total": 2,
  "authors": [
    {
      "name": "Qike Li"
    },
    {
      "name": "Fabio Perroni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mjhg43tfwe11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17494",
  "fulltext_url": null,
  "id": "8mjhg43tfwe11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17494",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213402749",
  "pdf_url": "https://arxiv.org/pdf/2609.17494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mjhg43tfwe11.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Equivariant Cohomological Crepant Resolution Conjecture for ADE-orbifolds",
  "title_text": "Equivariant Cohomological Crepant Resolution Conjecture for ADE-orbifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/8mjhg43tfwe11",
  "venue": "arXiv",
  "versions": []
}