A simple expression for the Casimir operator on a Lie group

Anderson, Mary F.

doi:10.1090/S0002-9939-1979-0545606-3

A simple expression for the Casimir operator on a Lie group
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Proc. Amer. Math. Soc. 77 (1979), 415-420 Request permission

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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