A plethystic chain rule

2025/08/05 by Alessandro D’Andrea, Alessandro D'Andrea, Enrico Fatighenti +4 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.2508.03568

openalex publication_date 2025/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a derivation D on the ring Λ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that D restricts to a quasi-isometry, with respect to the Hall product, on the graded component of Λ of each positive degree and provide a chain-rule formula with respect to the plethysm operation. Furthermore, we relate the geometry of the Schur functions supporting D(f), where f∈ Λ is an homogeneous symmetric function, to that of f.

Cited by

• Chern character of Schur bundles

Related

• A combinatorial proof of a plethystic Murnaghan--Nakayama rule
• Schur Functors and Categorified Plethysm
• Combinatorics and Representation Theory of Special Cases of Chern Plethysm
• Stability properties of inner plethyms (Lecture Notes)
• Splitting the square of homogeneous and elementary functions into their symmetric and anti-symmetric parts