Yang-Yang functions, monodromy and knot polynomials

We derive a structure of $\mathbb{Z}[t,t^{-1}]$-module bundle from family Yang-Yang functions. For the fundamental representation complex simple Lie algebra classical type, we give explicit wall-crossing formula and prove that monodromy is equivalent to braid group induced by universal R-matrices $U_{h}(g)$. show two transformations on fiber symmetry breaking deformation respectively rotation parameters commute with each other.