  We consider 3d $\mathcal{N} = 4$ theories on the geometry
$\Sigma\times\mathbb{R}$, where $\Sigma$ is a closed and connected Riemann
surface, from the point of view of a quantum mechanics on $\mathbb{R}$.
Focussing on the elementary mirror pair in the presence of real deformation
parameters, namely SQED with one hypermultiplet (SQED[1]) and the free
hypermulitplet, we study the algebras of local operators in the respective
quantum mechanics as well as their action on the vector space of supersymmetric
ground states. We demonstrate that the algebras can be described in terms of
Heisenberg algebras, and that they act in a way reminiscent of Segal-Bargmann
(B-twist of the free hypermultiplet) and Nakajima (A-twist of SQED[1])
operators.
