Cohomology of a flag variety as a Bethe algebra

We interpret the equivariant cohomology $H^*_{GL_n}(\mathcal{F}_{\boldsymbol\lambda},mathbb{C})$ of a partial flag variety $\mathcal{F}_{\boldsymbol\lambda}$ parametrizing chains of subspaces $0=F_0\subset F_1\subset\dots\subset F_N=\mathbb{C}^n$, $\dim F_i/F_{i-1}=\lambda_i$, as the Bethe algebra $\mathcal{B}^\infty(\mathcal{V}^\pm_{\boldsymbol\lambda})$ of the $\mathfrak{gl}_N$-weight subspace $\mathcal{V}^\pm_{\boldsymbol\lambda}$ of a $\mathfrak{gl}_N[t]$-module $\mathcal{V}^\pm$.