TL;DR
This paper investigates the properties of colored HOMFLY polynomials using skein theory, confirming predicted symmetries and limit behaviors, thus advancing mathematical understanding of knot invariants.
Contribution
It provides new proofs of symmetry and limit properties of colored HOMFLY polynomials within skein theory, aligning mathematical results with recent physics predictions.
Findings
Confirmed symmetries of colored HOMFLY polynomials
Established limit behaviors consistent with physicists' predictions
Enhanced understanding of knot invariants through skein theory
Abstract
In this paper, we study the properties of the colored HOMFLY polynomials via HOMFLY skein theory. We prove some limit behaviors and symmetries of the colored HOMFLY polynomial predicted in some physicists' recent works.
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