Symmetric Representation Rings are $\lambda$-Rings

TL;DR

This paper proves that the Grothendieck-Witt ring of symmetric representations of affine algebraic group schemes naturally forms a special λ-ring, extending the structure known for the usual representation ring.

Contribution

It establishes that the symmetric representation ring, specifically the Grothendieck-Witt ring, inherits a λ-ring structure for any affine algebraic group scheme over fields of characteristic not two.

Findings

Grothendieck-Witt ring of symmetric representations is a λ-ring.

The λ-ring structure applies to affine algebraic group schemes over characteristic not two.

Extends known λ-ring structure from representation rings to symmetric representation rings.

Abstract

The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $\lambda$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the representation category, for any affine algebraic group scheme over a field of characteristic not two.