  The stable envelopes of Okounkov et al. realize some representations of
quantum algebras associated to quivers, using geometry. We relate these
geometric considerations to quantum field theory. The main ingredients are the
supersymmetric interfaces in gauge theories with four supercharges, relation of
supersymmetric vacua to generalized cohomology theories, and Berry connections.
We mainly consider softly broken compactified three dimensional $\mathcal{N}
=4$ theories. The companion papers will discuss applications of this
construction to symplectic duality, Bethe/gauge correspondence, generalizations
to higher dimensional theories, and other topics.
