A new approach to the eigenvalues of the Gel’fand invariants for the unitary, orthogonal, and symplectic groups
- 1 January 1978
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 19 (1) , 164-167
- https://doi.org/10.1063/1.523535
Abstract
The expressions for the Gel’fand invariants (Casimir operators) of U(n), O(n), and Sp(n) in terms of the IR labels are derived by relating them to the trace of a suitably defined operator Pk. The method has unity and simplicity, since trace (Pk) can be related directly to the IR labels using the Weyl dimension function—without having to determine the eigenvectors of P.Keywords
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