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The Explicit Fourier Decomposition of L2SO(n)/SO(n - m))

Published online by Cambridge University Press:  20 November 2018

Robert S. Strichartz
Robert S. Strichartz*
Affiliation:
Cornell University, Ithaca, New York
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The decomposition of L2SO(n)/SO(n - m)) into a direct sum of irreducible representations of SO(n) is given abstractly by the branching theorem and the Frobenius reciprocity theorem [1]. The goal of this paper is to obtain this decomposition explicitly, generalizing the theory of spherical harmonics (m = 1). The case m = 2 has been studied in Levine [6], and the case 2m ≦ n in Gelbart [3]. Our results shed more light on these cases as well as revealing new phenomena which only occur when 2m > n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 294 - 310
Copyright
Copyright © Canadian Mathematical Society 1975

References

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