We will present conjectures about some scalar products of the XXX spin chain on the circle with a twist or on the segment (Belliard Pimenta 2015), namely the Slavnov and the Gaudin formulas. This result follows from the modified algebraic Bethe ansatz analysis (Belliard Crampé 2013, Belliard 2014) of the spectrum problem of the models. This result should be extended to other finites models that can be describe from the Yang Baxter and the Reflection equations. Importantly, we observe that the off-shell action of the transfer matrix on the Bethe vector and the ratio of the Slavnov and the Gaudin formulas are similar for the XXX and XXZ spin chains with or without U(1) symmetry and only differ from the eigenvalue and some U(1) invariant functions.

Cergy-Pontoise