On the structure of graded commutative exponential funtors

TL;DR

This paper studies the structure of graded commutative exponential functors and applies these insights to compute homology of symmetric groups and extensions in strict polynomial functors.

Contribution

It provides new structural results for graded commutative exponential functors and demonstrates their applications in homology and extension computations.

Findings

Computed homology of symmetric groups.

Determined extensions in strict polynomial functors.

Established structural properties of exponential functors.

Abstract

We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial functors.