On the Submodule Structure of Hook Specht Modules in Characteristic 2

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.