On the derived functors of the third symmetric-power functor

TL;DR

This paper computes the derived functors of the third symmetric-power functor and confirms previous predictions, advancing understanding in algebraic functor calculus.

Contribution

It provides explicit calculations of derived functors and cross-effects for the third symmetric-power, largely proving earlier conjectures.

Findings

Derived functors computed for specific cases

Results match previous predictions

Significant progress in symmetric-power functor theory

Abstract

We compute the derived functors of the third symmetric-power functor and their cross-effects for certain values. These calculations match predictions by the first named author and largely prove them in general.