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On the Branching Theorem of the Symplectic Groups

Published online by Cambridge University Press:  20 November 2018

C. Y. Lee
C. Y. Lee*
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby 2, B.C.
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In [1], Zhelobenko introduced the concept of a Gauss decomposition ZtDZ of a topological group and gave characterizations of irreducible representations of the classical groups. In this setting, vectors of representation spaces are polynomial solutions of a system of differential equations and the problem of obtaining branching theorem with respect to a subgroup G0 is to find all polynomial solutions that are invariant under Z ∩ G0 and have dominant weight with respect to D ∩ G0

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 535 - 545
Copyright
Copyright © Canadian Mathematical Society 1974

Footnotes

(1)

The results in this paper are contained in C. Y. Lee′s Ph.D. thesis, written under the guidance of Professor A. Das.

References

1. Zhelobenko, D. P., The classical groups. Spectral analysis of their finite-dimensional representations, Russian Math. Surveys 17 (1962), 1-94.Google Scholar
2. Lepowsky, thesis, J., M.I.T. (1970).Google Scholar
3. Lepowsky, J., Multiplicity formulas for certain semisimple Lie groups, Bull. Amer. Math. Soc. 4, vol. 77 (1971) 601-605.Google Scholar
4. Hegerfeldt, G. C., Branching theorem for the symplectic groups, J. Math. Phys. 8 (1967), 1195-1196.Google Scholar