English

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

Quantum Algebra 2015-03-09 v1 Combinatorics Representation Theory

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.

Keywords

Cite

@article{arxiv.1503.01882,
  title  = {On the existence of real R-matrices for virtual link invariants},
  author = {Guus Regts and Alexander Schrijver and Bart Sevenster},
  journal= {arXiv preprint arXiv:1503.01882},
  year   = {2015}
}