Arkiv för Matematik

, Volume 20, Issue 1–2, pp 69–85 | Cite as

Spherical functions and invariant differential operators on complex Grassmann manifolds

  • Bob Hoogenboom


Proofs are given of two theorems of Berezin and Karpelevič, which as far as we know never have been proved correctly. By using eigenfunctions of the Laplace-Beltrami operator it is shown that the spherical functions on a complex Grassmann manifold are given by a determinant of certain hypergeometric functions. By application of this result, it is proved that a certain system of operators, fow which explicit expressions are given, generates the algebra of radial parts of invariant differential operators.

Key Words & Phrases

Complex Grassmann manifold spherical function radial part of an invariant differential operator hypergeometric function Jacobi function 


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Copyright information

© Institut Mittag Leffler 1982

Authors and Affiliations

  • Bob Hoogenboom
    • 1
  1. 1.Mathematisch CentrumAmsterdamThe Netherlands

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