A new action of the Kudo-Araki-May algebra on the dual of the symmetric algebras, with applications to the hit problem (Q541309)

The ``hit problem'' for a module over the Steenrod algebra is to find a minimal set of generators for the module. Dually one looks for the ``primitive'' elements in the dual module -- those annihilated by all positive degree Steenrod operations. In this paper the authors give a new action of the Kudo-Araki-May algebra on the symmetric algebras over a field of \(p\) elements, and show how this can be used to construct new primitive elements from known ones. They note that it is non-trivial that their formulas respect the Adem relations in the Kudo-Araki-May algebra (and thus define an action of this algebra rather than its free analogue), and that they know of no geometric interpretation for their action.