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 a homogeneous element, to that of f.
D'Andrea, A., Fatighenti, E., Onorati, C. (2026). A Plethystic Chain Rule. ALGEBRAS AND REPRESENTATION THEORY, 0, 1-21 [10.1007/s10468-026-10411-7].
A Plethystic Chain Rule
D'Andrea A.
;Fatighenti E.;Onorati C.
2026
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 a homogeneous element, to that of f.File in questo prodotto:
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