An Explicit Construction of Casimir Operators and Eigenvalues:II

Details An Explicit Construction of Casimir Operators and Eigenvalues:II An Explicit Construction of Casimir Operators and Eigenvalues:II

1996-11-04

arxiv.org/abs/physics/9611002v4

J.Math.Phys. 38 (1997) 5991-6007

Physics

Mathematical Physics

16 pages, no figures, TeX file,the formulas (II.14) and (II.15) are corrected, change in e-mail address

Scientific paper

10.1063/1.532176

It is given a way of computing Casimir eigenvalues for Weyl orbits as well as for irreducible representations of Lie algebras. A kappa(s) number of polinomials which depend on rank N are obtained explicitly for A_N Casimir operators of order s where kappa(s) is the number of partitions of s into positive integers except 1. It is also emphasized that these eigenvalue polinomials prove useful in obtaining formulas to calculate weight multiplicities and in explicit calculations of the whole cohomology ring of Classical and also Exceptional Lie algebras.

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