{
  "id": "2103.06903",
  "version": "v1",
  "published": "2021-03-11T19:01:14.000Z",
  "updated": "2021-03-11T19:01:14.000Z",
  "title": "Pre-canonical bases on affine Hecke algebras",
  "authors": [
    "Nicolas Libesindky",
    "Leonardo Patimo",
    "David Plaza"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases $\\{\\mathbf{N}^i\\}_{1\\leq i \\leq m+1} $ (where $m$ is the height of the highest root) of the spherical Hecke algebra that interpolates between the standard basis $\\mathbf{N}^1$ and the canonical basis $\\mathbf{N}^{m+1}$. The expansion of $\\mathbf{N}^{i+1}$ in terms of the $\\mathbf{N}^i$ is in many cases very simple and we conjecture that in type $A$ it is positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T19:01:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine hecke algebras",
      "pre-canonical bases",
      "affine weyl group",
      "spherical hecke algebra",
      "highest root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}