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 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