rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Conformal Symmetry Breaking Operators for Differential Forms on Spheres
  name:
    name part: Kobayashi, Toshiyuki.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kubo, Toshihisa.
    role:
      role term: author.
  name:
    name part: Pevzner, Michael.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: si
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: IX, 192 p. online resource.
  abstract: This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.
  note: by Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Fourier analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Differential Geometry
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Mathematical Physics
  subject:
    topic: Fourier Analysis
  subject:
    topic: Partial Differential Equations
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2170
  identifier: 9789811026577
  identifier: http://dx.doi.org/10.1007/978-981-10-2657-7
  record info:
    record creation date: 161011
    record change date: 20161011121333.0
    record identifier: 978-981-10-2657-7