Affine strict polynomial functors and formality

TL;DR

This paper introduces affine strict polynomial functors to analyze the homological effects of Frobenius twist operations in positive characteristic, drawing analogies with algebraic loop group representations.

Contribution

It defines affine strict polynomial functors and demonstrates their utility in understanding Frobenius twist homology, linking to loop group representations.

Findings

Affine strict polynomial functors elucidate Frobenius twist homology.

The category shows an analogy with algebraic loop group representations.

Provides new tools for studying polynomial functors in positive characteristic.

Abstract

We introduce the notion of affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive characteristic. We also point out for an analogy between our category and the category of representations of the group of algebraic loops on $GL_n$.