2022/12/10 by Gruen, Angus
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2212.05222
For every knot K and lie algebra \mathfrakg, there is a Gukov-Manolescu series denoted F^\mathfrakgK which serves as an analytic continuation of the quantum knot invariants associated to finite dimensional irreducible representations of \mathfrakg. There has been a great deal of work done on computing this invariant for \mathfrakg = \mathfraksl2 but comparatively less work has studied other lie algebras. In this paper we extend the large colour R matrix from \mathfraksl2 to symmetrically coloured \mathfrakslN. This gives a definition for F^\mathfrakslN, symK for positive braid knots and allows for predictions of F^\mathfrakslN, symK for a much larger class of knots and links. It also provides further evidence towards a conjectural HOMFLY-PT analouge of FK.