  We present a simple but explicit example of a recent development which
connects quantum integrable models with Schubert calculus: there is a purely
geometric construction of solutions to the Yang-Baxter equation and their
associated Yang-Baxter algebras which play a central role in quantum integrable
systems and exactly solvable lattice models in statistical physics. We consider
the degenerate five-vertex limit of the asymmetric six-vertex model and
identify its associated Yang-Baxter algebra as convolution algebra arising from
the equivariant Schubert calculus of Grassmannians. We show how our method can
be used to construct (Schur algebra type) quotients of the current algebra
$\mathfrak{gl}_2[t]$ acting on the tensor product of copies of its evaluation
representation $\mathbb{C}^2[t]$. Finally we connect it with the COHA for the
$A_1$-quiver.
