发表机构
School of Mathematics and Statistics, Central China Normal University; Department of Mathematics and New Cornerstone Science Laboratory, The University of Hong Kong; School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education) & Shanghai Key Laboratory of PMMP, East China Normal University（华中师范大学数学与统计学院; 香港大学数学系及新Cornerstone科学实验室; 华东师范大学数学科学学院、教育部MEA重点实验室及上海PMMP重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究为经典群塔和 wreath 积群的表示范畴构建了统一的大范畴化框架，借助海森堡范畴与 Kac--Moody 2-范畴的作用，在特征零下控制群代数分次中心并区分不可约特征标，还得到 wreath 积群的模块描述。
AI 中文摘要
我们为有限经典群塔和 wreath 积群的表示范畴的“大”范畴化建立了一个统一框架。我们构造了海森堡范畴对称积的作用，在有限经典群情形下为量子海森堡范畴，在 wreath 积群情形下为退化海森堡范畴。这些作用导出了合适的 Kac--Moody 2-范畴对称积的范畴作用，进而导出了大李代数在格罗滕迪克群上的作用。在特征零情形下，所得作用通过图示中心元控制群代数的全部分次中心，且相关的着色权函数可区分所有不可约普通特征标。我们还通过范畴化得到了 wreath 积群的模块结构描述。
英文摘要
We develop a uniform framework for ``big'' categorification of representation categories of towers of finite classical groups and wreath product groups. We construct actions of symmetric products of Heisenberg categories, quantum in the finite classical group case and degenerate in the wreath product case. These actions lead to categorical actions of suitable symmetric products of Kac--Moody 2-categories, and hence to actions of large Lie algebras on Grothendieck groups. In characteristic zero, the resulting actions control the full graded centers of the group algebras through diagrammatic central elements, and the associated colored weight functions separate all irreducible ordinary characters. We also obtain modular block descriptions for wreath product groups through categorification.
CommentsImproved exposition and corrected Corollary 6.26
