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Spherical functions and invariant differential operators on complex Grassmann manifolds

Bob Hoogenboom Mathematisch Centrum, Kruislaan 413, Amsterdam, The Netherlands

TBD mathscidoc:1701.332555

Arkiv for Matematik, 20, (1), 69-85, 1980.10
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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[ Download ] [ 2017-01-08 20:35:12 uploaded by arkivadmin ] [ 1461 downloads ] [ 0 comments ] [ Cited by 20 ] 
@inproceedings{bob1980spherical,
  title={Spherical functions and invariant differential operators on complex Grassmann manifolds},
  author={Bob Hoogenboom},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203512078630364},
  booktitle={Arkiv for Matematik},
  volume={20},
  number={1},
  pages={69-85},
  year={1980},
}
Bob Hoogenboom. Spherical functions and invariant differential operators on complex Grassmann manifolds. 1980. Vol. 20. In Arkiv for Matematik. pp.69-85. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203512078630364.
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