Eigenvalues of Casimir Operators for the General Linear, the Special Linear, and the Orthosymplectic Lie Superalgebras

摘要

The generators of the algebras under consideration can be written in a canonical two-index form and hence the associated standard seuqence of Casimir elements can be constructed. Following the classical approach by Perelomov and Popov, we obtain the eigenvalues of these Casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions. (ERA citation 08:047929)