{
  "id": "1108.4379",
  "version": "v1",
  "published": "2011-08-22T17:05:05.000Z",
  "updated": "2011-08-22T17:05:05.000Z",
  "title": "Excursions into Algebra and Combinatorics at $q=0$",
  "authors": [
    "Tom Denton"
  ],
  "comment": "92 pages, 13 figures. PHd Dissertation accepted at the University of California on July 15th, 2011. arXiv admin note: text overlap with arXiv:1012.1361",
  "categories": [
    "math.RT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "We explore combinatorics associated with the degenerate Hecke algebra at $q=0$, obtaining a formula for a system of orthogonal idempotents, and also exploring various pattern avoidance results. Generalizing constructions for the 0-Hecke algebra, we explore the representation theory of $\\JJ$-trivial monoids. We then discuss two-tensors of crystal bases for $U_q(\\tilde{\\mathfrak{sl}_2})$, establishing a complementary result to one of Bandlow, Schilling, and Thi\\'ery on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for simply-laced crystal bases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-22T17:05:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorics",
      "excursions",
      "degenerate hecke algebra",
      "stembridges local axioms",
      "computer implementation"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 92,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4379D"
    }
  }
}