I've been asked to determine the eigenvalue of the Casimir invariant $I_2$ on any irreducible module with highest weight $\lambda = (\lambda_1, \lambda_2, ..., \lambda_n)$, where; $$I_m = \sum^{n}_{k=1}A^{m}_{kk}$$With $A^{m}_{kk}$ being a representation for the diagonal elements of the universal enveloping algebra $U(gl(n))$. I'm not really sure where to start with it, and any help would be fantastic.
2026-05-05 20:27:37.1778012857
Casimir Invariants within the universal enveloping algebra
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