标题： 关于由Steinberg模的限制生成的初等p群的张量理想的一个猜想 显示英文标题

标题： A conjecture on the tensor ideal for an elementary p-group generated by the restriction of a Steinberg module

摘要： 在以前的工作（Coulembier--Flake 2024）中，作者猜想，任意有限维模表示的初等交换$p$-群与最大的非投射限制 Steinberg$SL_2$-模的张量积是一个限制倾斜模。 我们表明，该猜想的有效性将在正特征的张量范畴理论中产生有趣的含义，特别是关于不可压缩对称张量范畴的分类，这是该领域 arguably 最主要的开放猜想的主题。 我们在这里提供了一些支持该猜想成立的证据。 显示英文摘要

摘要： In previous work (Coulembier--Flake 2024), the authors conjectured that the tensor product of an arbitrary finite-dimensional modular representation of an elementary abelian $p$-group with the biggest non-projective restricted Steinberg $SL_2$-module is a restricted tilting module. We showed that the validity of the conjecture would have interesting implications in the theory of tensor categories in positive characteristic, in particular, with respect to the classification of incompressible symmetric tensor categories, which is the subject of arguably the main open conjecture in the area. We present here some evidence for the conjecture to hold.