Remember that 
should take values in some representation 
of the bosonic
group, so in constructing the covariant exressions we should take into account the structure
of .
We assume 2 things about :
The quadratic Casimir of 
vanishes (this is the difference of the two Casimirs)
Exists a vector 
invariant under 
These two conditions are actually quite restrictive.
The first condition implies that contained in the decomposition of functions on 
.
The second condition implies that it is actually contained in the harmonic functions.
: preliminaries