Recognition: unknown
On universal knot polynomials
read the original abstract
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representation. Properties of universal polynomials and applications of these results are discussed.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Racah matrices for the symmetric representation of the SO(5) group
Explicit R and Racah matrices are given for the symmetric representation of SO(5) to compute Kauffman polynomials via a generalized Reshetikhin-Turaev construction.
-
A relation between the HOMFLY-PT and Kauffman polynomials via characters
HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.
-
Diagrammatic technique for Vogel's universality
Vogel's diagrammatic Lambda-algebra enables truly universal computations of Lie-theoretic quantities, demonstrated via multiple examples.
-
A note on universality in refined Chern-Simons theory
Refined Chern-Simons theory universality is restricted to simply laced Lie groups, unlike the original which applies to all simple Lie groups.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.