Let G be a connected reductive complex algebraic group, and E a complex elliptic curve. Let $G_E$ denote the connected component of the trivial bundle in the stack of semistable G-bundles on E. We introduce a complex analytic uniformization of $G_E$ by adjoint quotients of reductive subgroups of the loop group of G. This can be viewed as a nonabelian version of the classical complex analytic uniformization $E\simeq {\mathbb{C}}^{⁎}/q^{\mathbb{Z}}$. We similarly construct a complex analytic uniformization of G itself via the exponential map, providing a nonabelian version of the standard isomorphism ${\mathbb{C}}^{⁎}\simeq \mathbb{C}/\mathbb{Z}$, and a complex analytic uniformization of $G_E$ generalizing the standard presentation $E\simeq \mathbb{C}/(\mathbb{Z}\oplus \mathbb{Z}\tau )$. Finally, we apply these results to the study of sheaves with nilpotent singular support. As an application to Betti geometric Langlands conjecture in genus 1, we define a functor from $S{h}_{\mathcal{N}}(G_E)$ (the semistable part of the automorphic category) to ${\mathrm{\text{IndCoh}}}_{\check{\mathcal{N}}}({\mathrm{\text{Locsys}}}_{\check{G}}(E))$ (the spectral category).

令G为连接的还原复代数群，E为复椭圆曲线。让$G_{Ë}$表示E上的半稳定G束堆栈中平凡束的连接分量。我们介绍了一个复杂的分析统一$G_{Ë}$G的环群的还原子群的伴随商。可以将其视为经典复杂分析均匀化的非阿贝尔版本$Ë\simeq {\mathbb{C}}^{⁎}/q^{\mathbb{ž}}$。我们同样通过指数图构造G本身的复杂解析均匀化，从而提供标准同构的非阿贝尔版本${\mathbb{C}}^{⁎}\simeq \mathbb{C}/\mathbb{ž}$，以及的复杂解析统一 $G_{Ë}$ 概括标准介绍 $Ë\simeq \mathbb{C}/（\mathbb{ž}\oplus \mathbb{ž}\tau ）$。最后，我们将这些结果应用于零幂奇异支撑的滑轮的研究。作为对属1的Betti几何Langlands猜想的一种应用，我们定义了一个$\mathrm{小号}{H}_{\mathcal{ñ}}（G_{Ë}）$ （自同构类别的半稳定部分） ${\mathrm{\text{印度}}}_{\check{\mathcal{ñ}}}（{\mathrm{\text{洛克思}}}_{\check{G}}（Ë））$ （光谱类别）。