A Simple Expression for the Casimir Operator on a Lie Group
Copyright policy )A Simple Expression for the Casimir Operator on a Lie Group
The expression for the Casimir operator for a real semisimple Lie group G in terms of coordinates given by the Iwasawa decomposition G = K A N 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.
Analysis on real and complex Lie groups, Semisimple Lie groups and their representations, principal series representations, Casimir operator, real semisimple Lie group, Iwasawa decomposition
Analysis on real and complex Lie groups, Semisimple Lie groups and their representations, principal series representations, Casimir operator, real semisimple Lie group, Iwasawa decomposition
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