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math-ph2025
Braid twists and HZ factorisation via character expansion
Andreani Petrou, Shinobu Hikami
The HOMFLY-PT polynomial of a closed braid admits a character expansion, expressed as a sum of SU(N) characters over Young diagrams. The Harer-Zagier (HZ) transform, which converts…
math-ph2024
The HOMFLY-PT polynomial and HZ factorisation
Andreani Petrou, Shinobu Hikami
The Harer-Zagier (HZ) transform maps the HOMFLY-PT polynomial into a rational function. For some special knots and links, the latter admits a simple factorised form, which is refer…
math-ph2023
Harer-Zagier formulas for families of twisted hyperbolic knots
Andreani Petrou, Shinobu Hikami
In an attempt to generalise knot matrix models for non-torus knots, which currently remains an open problem, we derived formulas for the Harer-Zagier transform of the HOMFLY-PT pol…