Higher spin representations of the Yangian of sl₂ and R-matrices

We study higher spin (pure and mixed spin) representations of the Yangian of sl₂. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin BZJ20. When the framing dimension is 1, it recovers the evaluation pullback of the +1-dimensional irreducible representation of sl₂. We introduce the lattice model and prove that its partition function coincides with the weight function constructed using the framed shuffle formula. The latter follows the approach of Rim\'anyi, Tarasov and Varchenko RTV15.