Abstract
The entire Casimir operator on a real semisimple Lie group is expressed in convenient forms related to the Iwasawa, Bruhat, and Cartan decompositions of the group. Its restriction to G/N may be realized as an operator with constant coefficients on A, and its restriction to G/K, which is the Laplacian on G/K, is expressed as a polynomial differential operator on the Borel subgroup AN. Similar results are proved for higher order bi-invariant operators on G. In addition, explicit polynomial expressions for the generators of the centers of the enveloping algebras of a2, and b2 (= c2) are found.
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References
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© 1981 Springer-Verlag
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Anderson, M.J. (1981). Explicit expressions for the generators of the center of the enveloping algebra of real lie algebras and for the algebra of bivariant operators on the group. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090558
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DOI: https://doi.org/10.1007/BFb0090558
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