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arXiv · 1503.01882

On the existence of real R-matrices for virtual link invariants

Guus Regts·Alexander Schrijver·Bart Sevenster
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Abstract

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.

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Guus Regts, Alexander Schrijver, Bart Sevenster. 2015-03-06. On the existence of real R-matrices for virtual link invariants. https://arxiv.org/abs/1503.01882

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