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The invariant polynomial algebras for the groups ISL(n) and ISp(n)

Published online by Cambridge University Press:  22 January 2016

Hitoshi Kaneta
Hitoshi Kaneta*
Affiliation:
Faculty of Education Tokushima University, Tokushima 770, Japan
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This paper is a continuation to the previous one [3], We shall show that, for the inhomogeneous linear group ISL(n + 1, R) (resp. ISp(n, R)), the coadjoint invariant polynomial algebra is generated by one (resp. n) algebraically independent element. We shall state our results more precisely.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 94 , June 1984 , pp. 61 - 73
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Abellanas, L. and Alonso, L. Martinez, A general setting for Casimir invariants, J. Math. Phys., 16 (1975), 1580–1584.CrossRefGoogle Scholar
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[ 3 ] Kaneta, H., The invariant polynomial algebras for the groups IU(n) and ISO(n) , Nagoya Math. J., 94 (1984), 43–59.CrossRefGoogle Scholar
[ 4 ] Varadarajan, V. S., Lie groups, Lie algebras and their representations, Prentice-Hall, Inc., London 1974.Google Scholar
[ 5 ] Warner, G., Harmonic analysis on semi-simple Lie groups I, Springer-Verlag 1972.Google Scholar
[ 6 ] Perroud, M., The fundamental invariants of inhomogeneous classical groups, J. Math. Phys., 24 (1983), 1381–1391.CrossRefGoogle Scholar