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We generalize Aganagic-Okounkov's theory of elliptic stable envelopes, andits physical realization in Dedushenko-Nekrasov's and Bullimore-Zhang's works,to certain varieties without holomorphic symplectic structure or polarization.These classes of varieties include, in particular, classical Higgs branches of3d $\mathcal N=2$ quiver gauge theories. The Bethe/Gauge Correspondence relatessuch a gauge theory to an anisotropic/elliptic superspin chain, and the stableenvelopes compute the R-matrix that solves the dynamical Yang-Baxter equation(dYBE) for this spin chain. As an illustrative example, we solve the dYBE forthe elliptic $\mathfrak{sl}(1|1)$ spin chain with fundamental representationsusing the corresponding 3d $\mathcal N=2$ SQCD whose classical Higgs branch isthe Lascoux resolution of a determinantal variety. Certain Janus partitionfunctions of this theory on $I \times \mathbb E$ for an interval $I$ and anelliptic curve $\mathbb E$ compute the stable envelopes, and in turn thegeometric R-matrix, of the $\mathfrak{sl}(1|1)$ spin chain. Furthermore, weconsider the 2d and 1d reductions of elliptic stable envelopes and theR-matrix. The reduction to 2d gives the K-theoretic stable envelopes and thetrigonometric R-matrix, and a further reduction to 1d produces thecohomological stable envelopes and the rational R-matrix. The latter recoversthe results of Rim\'anyi and Rozansky.

Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical R-Matrices for Superspin Chains from The Bethe/Gauge Correspondence