So, it turns out that we should take affine transversal slice to closure of an $G(\mathcal{O})$ orbit in affine grassmanian $G(K) / G(\mathcal{O})$, then there is "some" $X$ of smallest dimension in this slice, which is of our interest. $X$ turns out to be a singular variety (e.g. $\mathbb{C}^{2} / (\mathbb{Z} / n\mathbb{Z})$). Let $\widetilde{X} \to X$ be it's minimal resolution. We take quantum cohomology of $\widetilde{X}$ and see how basis forms of $H^{2}_{q}(X)$ act on the whole $H^{*}_{q}$ and these guys give rise to a connection which is Trigonometric Knizhnik-Zamolodchikov connection.

Yeah, rather complicated story which i surely incorrectly rewrote (and can't find reference). Okounkov said that this was proven in PhD thesis of one of his students.