Short adjointness-based proofs of universal-character SXP rules

Establish whether the adjoint relationship between the Verschiebung operator and plethysm by a power sum can yield short proofs of the SXP rules for universal symplectic and orthogonal characters.

Background

The paper notes that, for Schur functions, the adjoint relationship between the Verschiebung operator and plethysm provides a direct route between factorisation identities and SXP rules. It remains unresolved whether an analogous strategy can produce short proofs for universal-character SXP rules, because universal characters are not orthonormal under the Hall inner product.