发表机构
École Polytechnique Fédérale de Lausanne (EPFL); Simion Stoilow Institute of Mathematics (IMAR); Purdue University（洛桑联邦理工学院; 西米翁·斯托伊洛数学研究所; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了B、C、D型量子仿射超代数的shuffle实现，发展了A类超型灌木理论，定义了对应量子环面超代数，还提出了带参数箭图下shuffle实现的通用框架。
AI 中文摘要
我们证明了B、C、D型量子仿射超代数在圈实现下的 shuffle 实现，即我们在这些代数与适当定义的双 shuffle 代数之间构造一个同构。我们利用某些消失条件明确描述了后一类 shuffle 代数，这些条件推广了Feigin-Odesskii 轮子条件；一个新特征是出现了所谓的“可怕的轮子”，这是一个涉及7个变量的特定2阶消失条件。在此过程中，我们全面发展了A类超型（仿射和环面）中灌木的理论，灌木是研究与环面Calabi-Yau三维簇相关的shuffle代数的重要组合工具。我们的技术还使我们能够定义B、C、D型量子环面超代数。更重要的是，我们提供了一个通用框架，用于在带参数的箭图的广泛范围内表述和证明 shuffle 实现。
英文摘要
We prove the shuffle realization for quantum affine superalgebras of types $B,C,D$ in the loop realization, in that we construct an isomorphism between each of these algebras and a suitably defined double shuffle algebra. We explicitly describe the latter shuffle algebra using certain vanishing conditions that generalize the Feigin-Odesskii wheel conditions; a novel feature is the appearance of a so-called scary wheel, which is a particular order $2$ vanishing condition involving $7$ variables. Along the way, we fully develop the theory of shrubs in super types $A$ (affine and toroidal), which are important combinatorial tools in the study of the shuffle algebras associated to toric Calabi-Yau threefolds. Our techniques also allow us to define quantum toroidal superalgebras of types $B,C,D$. More importantly, we provide a general framework to formulate and prove shuffle realizations in the wide generality of quivers with parameters.
