Are the eigenvalues of the Casimir of the lie algebra continuous if the corresponding lie group is noncompact and discrete is the lie group is compact ? One example I know is $SU(2)$ group, the Casimir of its corresponding lie algebra is discrete and are labelled by $j \in \mathbb{N}$ while the Casimir of the Lorentz algebra is continuous and is labelled by $m \in \mathbb{R}^{+}$. Is this a general fact ? If so, how do we prove it ?
2026-04-01 06:09:04.1775023744
Casimirs of Lie Algebras
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