Polynomial functors in Ver₄⁺

2025/10/20 by Coulembier, Kevin, Hu, Serina
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.18175

Abstract

We study polynomial functors in the incompressible category Ver₄⁺, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how simple polynomial functors evaluate on arbitrary objects. We also determine which objects are not annihilated by any polynomial functors of a given degree and for which objects the symmetric group algebra acts faithfully via the braiding.

Citations

• Group schemes and their Lie algebras over a symmetric tensor category
• Super invariant theory in positive characteristic
• On Frobenius exact symmetric tensor categories

Related

• Polynomial functors on some categories of elements
• Polynomial Functors on Pointed Categories
• A comparison of twisted coefficient systems
• On finiteness properties of polynomial functors
• On homological properties of strict polynomial functors of degree p