{
  "id": "1606.07379",
  "version": "v1",
  "published": "2016-06-23T17:27:53.000Z",
  "updated": "2016-06-23T17:27:53.000Z",
  "title": "Separately Radial and Radial Toeplitz Operators on the Projective Space and Representation Theory",
  "authors": [
    "R. Quiroga-Barranco",
    "A. Sanchez-Nungaray"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider separately radial (with corresponding group $\\mathbb{T}^n$) and radial (with corresponding group $\\mathrm{U}(n))$ symbols on the projective space $\\mathbb{P}^n(\\mathbb{C})$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^*$-algebras generated by each family of such Toeplitz operators are commutative. We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the $C^*$-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method extends the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between $\\mathbb{T}^n$ and $\\mathrm{U}(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-23T17:27:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "32A36",
      "22E46",
      "32M15"
    ],
    "keywords": [
      "radial toeplitz operators",
      "separately radial",
      "projective space",
      "representation theory",
      "corresponding group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}