Mathematics – Geometric Topology
Scientific paper
2010-10-15
Mathematics
Geometric Topology
12 pages and 1 figure
Scientific paper
Rosso and Jones gave a formula for the colored Jones polynomial of a torus knot, colored by an irreducible representation of a simple Lie algebra. The Rosso-Jones formula involves a plethysm function, unknown in general. We provide an explicit formula for the second plethysm of an arbitrary representation of $\fsl_3$, which allows us to give an explicit formula for the colored Jones polynomial of the trefoil, and more generally, for T(2,n) torus knots. We give two independent proofs of our plethysm formula, one of which uses the work of Carini-Remmel. Our formula for the $\fsl_3$ colored Jones polynomial of T(2,n) torus knots allows us to verify the Degree Conjecture for those knots, to efficiently the $\fsl_3$ Witten-Reshetikhin-Turaev invariants of the Poincare sphere, and to guess a Groebner basis for recursion ideal of the $\fsl_3$ colored Jones polynomial of the trefoil.
Garoufalidis Stavros
Morton Hugh
Vuong Thao
No associations
LandOfFree
The SL_3 colored Jones polynomial of the trefoil does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The SL_3 colored Jones polynomial of the trefoil, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The SL_3 colored Jones polynomial of the trefoil will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-204021