  The irreducible representations of SU(N) over a mixed quark-antiquark Fock
space component have been studied for many years. In analogy to the case for
the quark-only Fock space component, there exist efficient tools to classify
the irreducible representations of SU(N) over a mixed tensor product space
using tableaux. Unlike the quark-only case, the only general algorithm known to
us for constructing the associated projection operators onto irreducible
multiplets involves translating N-1 fundamental factors into an antifundamental
factor using the Leibniz rule, which turns out to be computationally extremely
inefficient. If one is interested only in singlets, this problem can be
entirely avoided as is demonstrated below where we provide an efficient
algorithm to construct the projection operatators onto the irreducible
representations of dimension 1 of the special unitary group SU(N) over a mixed
Fock space component that transparently gives access to N dependence, and
discuss the relative merits in comparison to an alternative algorithm briefly
discussed in a different context by Keppeler and Sjoedahl.
