On Hopf-induced deformation of topological locus

TL;DR

This paper reviews the colored invariants of the Hopf link, focusing on a special deformation of the topological locus, and extends the description to conjugate, composite, and adjoint representations.

Contribution

It introduces an extended description of the topological locus for colored invariants, including conjugate, composite, and adjoint representations, enhancing the understanding of Hopf link invariants.

Findings

Extended the topological locus to conjugate representations

Defined adjoint Schur functions in the dual description

Provided a comprehensive review of colored invariants for the Hopf link

Abstract

We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations associated with the two components of the link. Most important, we extend the description of this locus to conjugate and, generically, to composite representations and also define the "adjoint" Schur functions emerging in the dual description.