无装饰编织簇的旋转不动点与仿射李代数的融合环
Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras
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中文总结 AI 辅助
本文证明无装饰编织簇上由循环旋转诱导的 Zamolodchikov 变换的不动点栈的粗模空间同构于相应仿射李代数的融合环的谱，并推广至扭曲 Coxeter 元素，从而得到所有仿射李代数的融合环。
中文摘要 AI 辅助
设 $G$ 为单连通半单代数群。在与 Coxeter 元素的幂相关联的（无装饰）编织簇上，存在一个有限阶自等价，称为 Zamolodchikov 变换，由词的循环旋转诱导。本文证明，该自等价的不动点栈的粗模空间同构于相应仿射李代数的融合环的谱。上述结果也推广到扭曲 Coxeter 元素，并且所有仿射李代数的融合环均以此方式获得。
英文摘要
Let $G$ be a simply connected semisimple algebraic group. On the (undecorated) braid variety associated with a power of a Coxeter element, there is a finite-order autoequivalence, called the Zamolodchikov transformation, induced by cyclic rotation of words. In this paper, we show that the coarse moduli space of the fixed-point stack of this autoequivalence is isomorphic to the spectrum of the fusion ring of the corresponding affine Lie algebra. The above results also extend to twisted Coxeter elements, and the fusion rings of all affine Lie algebras are obtained in this way.
