Multivariable link invariants arising from sl(2|1) and the Alexander polynomial
Geometric Topology
2007-05-23 v2 Quantum Algebra
Abstract
In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link invariant. This new invariant can be thought of as a multivariable version of the Links-Gould invariant. We also show that after a variable reduction our invariant specializes to the Conway potential function, which is a version of the multivariable Alexander polynomial.
Cite
@article{arxiv.math/0601291,
title = {Multivariable link invariants arising from sl(2|1) and the Alexander polynomial},
author = {Nathan Geer and Bertrand Patureau-Mirand},
journal= {arXiv preprint arXiv:math/0601291},
year = {2007}
}
Comments
19 pages, to appear in Journal of Pure and Applied Algebra. Several changes and a proof added. (see math.GT/0609034 for other Lie superalgebras)