On strict polynomial functors: monoidal structure and Cauchy filtration. (Ergänzte Version)

Aquilino C. On strict polynomial functors: monoidal structure and Cauchy filtration. (Ergänzte Version). Bielefeld: Universität Bielefeld; 2016.The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. In the first part of this thesis we investigate this monoidal structure by considering the category of representations of the symmetric group which admits a tensor product coming from its Hopf algebra structure. It is known that there exists a functor *F* from the category of strict polynomial functors to the category of representations of the symmetric group. We show that *F* is monoidal. In the second part we explain the Cauchy filtration in the framework of strict polynomial functors. This filtration can be seen as the categorification of the Cauchy Formula for symmetric functions and is an important ingredient of the highest weight structure of the category of strict polynomial functors