Abstract:We consider a derivation $\mathsf{D}$ on the ring $\Lambda$ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that $\mathsf{D}$ restricts to a quasi-isometry, with respect to the Hall product, on the graded component of $\Lambda$ 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 $\mathsf{D}(f)$, where $f\in \Lambda$ is an homogeneous symmetric function, to that of $f$.
From: Claudio Onorati [view email]
[v1]
Tue, 5 Aug 2025 15:37:16 UTC (18 KB)
[v2]
Wed, 8 Oct 2025 19:56:34 UTC (19 KB)
[v3]
Sat, 18 Jul 2026 11:15:19 UTC (21 KB)
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