Invariant tensors and Casimir operators for simple compact Lie groups
Mathematical Physics
2009-10-31 v2 High Energy Physics - Theory
math.MP
Abstract
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing non-primitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.
Cite
@article{arxiv.physics/9802012,
title = {Invariant tensors and Casimir operators for simple compact Lie groups},
author = {A. J. Mountain},
journal= {arXiv preprint arXiv:physics/9802012},
year = {2009}
}
Comments
11 pages, LaTeX, minor changes, version in J. Math. Phys