Adams operators and knot decorations

Details Adams operators and knot decorations Adams operators and knot decorations

1997-11-19

arxiv.org/abs/q-alg/9711015v1

Mathematics

Quantum Algebra

Latex2e 26 pages with six figures

Scientific paper

We use an explicit isomorphism from the representation ring of the quantum group U_q(sl(N)) to the Homfly skein of the annulus, to determine an element of the skein which is the image of the mth Adams operator, \psi_m, on the fundamental representation, c_1. This element is a linear combination of m very simple m-string braids. Using this skein element, we show that the Vassiliev invariant of degree n in the power series expansion of the U_q(sl(N)) quantum invariant of a knot coloured by \psi_m(c_1) is the canonical Vassiliev invariant with weight system W_n\psi_m^{(n)} where W_n is the weight system for the Vassiliev invariant of degree n in the expansion of the quantum invariant of the knot coloured by c_1 and \psi_m^{(n)} is the Adams operator on n-chord diagrams defined by Bar-Natan.

Affiliated with

Also associated with

No associations

Rating

Adams operators and knot decorations 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 Adams operators and knot decorations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adams operators and knot decorations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-461039