Arkiv för Matematik

  • Ark. Mat.
  • Volume 20, Number 1-2 (1982), 69-85.

Spherical functions and invariant differential operators on complex Grassmann manifolds

Bob Hoogenboom

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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.

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Ark. Mat. Volume 20, Number 1-2 (1982), 69-85.

Received: 27 October 1980
First available in Project Euclid: 31 January 2017

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1982 © Institut Mittag Leffler


Hoogenboom, Bob. Spherical functions and invariant differential operators on complex Grassmann manifolds. Ark. Mat. 20 (1982), no. 1-2, 69--85. doi:10.1007/BF02390499.

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