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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A simple expression for the Casimir operator on a Lie group


Author: Mary F. Anderson
Journal: Proc. Amer. Math. Soc. 77 (1979), 415-420
MSC: Primary 22E46
DOI: https://doi.org/10.1090/S0002-9939-1979-0545606-3
MathSciNet review: 545606
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Abstract: The expression for the Casimir operator for a real semisimple Lie group G in terms of coordinates given by the Iwasawa decomposition $ G = KAN$ reduces on G/N to the difference of an elliptic operator with constant coefficients on A and an invariant operator on M. This result immediately identifies the principal series of induced representations with representations defined on the eigenspaces of the restriction of the Casimir operator to G/N.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0545606-3
Article copyright: © Copyright 1979 American Mathematical Society