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}
}