  Virtual links were introduced by Kauffman in 1999. We characterize the
virtual link invariants that are partition functions of vertex models (as
considered by de la Harpe and Jones), both in the real and in the complex case.
We show that for any fixed number of states, these invariants form an affine
variety. Basic techniques are the first and second fundamental theorem of
invariant theory for the orthogonal group (in the sense of Weyl) and some
related methods from algebraic geometry.

Quantum Algebra;Combinatorics;Geometric Topology