AI 中文总结
该研究在正特征域上有限群的Drinfel'd双情形下，计算映射类群在导出块空间上的作用，证明其与普通块空间上的映射类群表示通常不同，拓展了映射类群作用的相关研究。
AI 中文摘要
在本工作的第一部分中，我们针对不一定半单的模范畴，将曲面映射类群在共形块空间上的作用推广到所谓的导出块空间。在本文呈现的第二部分中，我们针对正特征域上有限群的Drinfel'd双明确计算该作用。为此，我们将Lyubashenko的映射类群表示方法与表示簇理论相联系，借此证明导出块空间上的映射类群表示通常不同于普通块空间上的此类表示。
英文摘要
In the first part of this work, we have, for a not necessarily semisimple modular category, generalized the action of the mapping class groups of surfaces on the spaces of conformal blocks to the so-called derived block spaces. In the second part presented here, we compute this action explicitly in the case of Drinfel'd doubles of finite groups over fields of positive characteristic. To do that, we connect Lyubashenko's approach to mapping class group representations with the theory of representation varieties. In this way, we are able to show that the mapping class group representations on the derived block spaces are in general different from those on the ordinary block spaces.
Comments105 pages, uses tikz-cd package
