Arkiv för Matematik
- Ark. Mat.
- Volume 20, Number 1-2 (1982), 69-85.
Spherical functions and invariant differential operators on complex Grassmann manifolds
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.
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. http://projecteuclid.org/euclid.afm/1485896970.