  The algebraic engineering technique is applied to a class of 3D
$\mathcal{N}=2$ gauge theories on the omega-deformed background
$\mathbb{R}_\epsilon^2\times S^1$. The vortex partition function and the
fundamental qq-character are obtained from a network of intertwiners between
representations of the shifted (or asymptotic) quantum affine
$\mathfrak{sl}(2)$ algebra. This network involves two types of representations,
the prefundamental representation of Hernandez-Jimbo, and a new vertex
representation acting on a bosonic Fock space. The brane system associated to
this network is identified: D3 branes carry the prefundamental module while
NS5-branes (+D5) support the Fock module. In the process, we highlight the role
of shifted quantum algebras in implementing the Higgsing procedure.
