{
  "id": "1101.3192",
  "version": "v3",
  "published": "2011-01-17T12:23:10.000Z",
  "updated": "2011-09-09T15:29:26.000Z",
  "title": "On homomorphisms indexed by semistandard tableaux",
  "authors": [
    "Sinead Lyle"
  ],
  "comment": "32 pages. This third version of the paper contains some comments on homomorphisms between the Specht modules defined by Dipper and James and has a more rigorous proof of the result following Proposition 4.1",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the homomorphism spaces between Specht modules for the Hecke algebras $\\h$ of type $A$. We prove a cellular analogue of the kernel intersection theorem and a $q$-analogue of a theorem of Fayers and Martin and apply these results to give an algorithm which computes the homomorphism spaces $\\Hom_{\\h}(S^\\mu,S^\\lambda)$ for certain pairs of partitions $\\lambda$ and $\\mu$. We give an explicit description of the homomorphism spaces $\\Hom_\\h(S^\\mu,S^\\lambda)$ where $\\h$ is an algebra over the complex numbers, $\\lambda=(\\lambda_1,\\lambda_2)$ and $\\mu$ is an arbitrary partition with $\\mu_1 \\geq \\lambda_2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-09T15:29:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semistandard tableaux",
      "homomorphisms",
      "homomorphism spaces",
      "kernel intersection theorem",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.3192L"
    }
  }
}