Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism

We prove that normalized colored Alexander polynomial (the \(A \rightarrow 1\) limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution \(q \rightarrow q^{|R|}\). The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices.