  We characterize the virtual link invariants that can be described as
partition function of a real-valued R-matrix, by being weakly reflection
positive. Weak reflection positivity is defined in terms of joining virtual
link diagrams, which is a specialization of joining virtual link diagram
tangles. Basic techniques are the first fundamental theorem of invariant
theory, the Hanlon-Wales theorem on the decomposition of Brauer algebras, and
the Procesi-Schwarz theorem on inequalities for closed orbits.
