{
  "id": "1309.5055",
  "version": "v2",
  "published": "2013-09-19T17:21:06.000Z",
  "updated": "2015-04-24T13:06:26.000Z",
  "title": "Schubert calculus and torsion explosion",
  "authors": [
    "Geordie Williamson"
  ],
  "comment": "21 pages, v2: proofs contain more detail, added an appendix with Kontorovich and McNamara proving exponential growth of torsion",
  "categories": [
    "math.RT"
  ],
  "abstract": "We observe that certain numbers occurring in Schubert calculus for SL_n also occur as entries in intersection forms controlling decompositions of Soergel bimodules and parity sheaves in higher rank. These numbers grow exponentially. This observation gives many counterexamples to Lusztig's conjecture on the characters of simple rational modules for SL_n over a field of positive characteristic. We explain why our examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-19T17:21:06.000Z",
      "title": "Schubert calculus and torsion",
      "abstract": "We observe that certain numbers occurring in Schubert calculus for SL_n also occur as entries in intersection forms controlling decompositions of Soergel bimodules and parity sheaves in higher rank. These numbers grow exponentially in the rank. This observation gives many counterexamples to Lusztig's conjecture on the characters of simple rational modules for SL_n over a field of positive characteristic. We explain why our examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.",
      "comment": "16 pages. preliminary version, comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-24T13:06:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C33",
      "20G05",
      "20G43"
    ],
    "keywords": [
      "schubert calculus",
      "intersection forms controlling decompositions",
      "simple rational modules",
      "soergel bimodules",
      "parity sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5055W"
    }
  }
}