arXiv subjects
Publications and source records attributed to Zain Ahmed Kapadia.
We classify which 2-part Young modules in characteristic 2 are uniserial, and which hook Specht modules in characteristic 2 are direct sums of uniserial summands. This is a continuation of the author's previous work [arxiv:2405.02039].
The submodule structure of general Specht modules in prime characteristic is a difficult open problem. Kleshchev and Sheth [Journal of Algebra, 221(2), pp.705-722] gave a combinatorial description of the submodule structure of Specht modules labelled by $2$-part partitions in prime characteristic. Using this result, as well as filtrations of Specht modules labelled by hook partitions via $2$-part Specht modules in characteristic $2$, one can study the submodule structure of hook Specht modules. In particular, we classify which of these are uniserial.