Koszul, Ringel, and Serre duality for strict polynomial functors

TL;DR

This paper explores dualities in the category of strict polynomial functors, including Koszul, Ringel, and Serre dualities, and clarifies their underlying monoidal structures, linking them to algebraic dualities.

Contribution

It explicitly describes the monoidal structure underlying Koszul duality and connects it to Ringel and Serre dualities in the context of strict polynomial functors.

Findings

Explicit description of the monoidal structure for Koszul duality

Connection established between Koszul, Ringel, and Serre dualities

Insights into the duality structures of Schur algebras

Abstract

This is a report on recent work of Chalupnik and Touze. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors.