2 research outputs found
Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations
This paper deals with the striking fact that there is an essentially
canonical path from the -th Lie algebra cohomology cocycle, ,
of a simple compact Lie algebra \g of rank to the definition of its
primitive Casimir operators of order . Thus one obtains a
complete set of Racah-Casimir operators for each \g and nothing
else. The paper then goes on to develop a general formula for the eigenvalue
of each valid for any representation of \g, and thereby
to relate to a suitably defined generalised Dynkin index. The form of
the formula for for is known sufficiently explicitly to make
clear some interesting and important features. For the purposes of
illustration, detailed results are displayed for some classes of representation
of , including all the fundamental ones and the adjoint representation.Comment: Latex, 16 page