Relationships between plethysm coefficients
Melanie de Boeck
TL;DR
This paper investigates the relationships between plethysm coefficients in the context of symmetric group representations, providing new insights into the structure of twisted Foulkes modules and their composition multiplicities.
Contribution
It establishes novel relationships between plethysm coefficients and composition multiplicities of twisted Foulkes modules, advancing understanding in symmetric function theory.
Findings
New relationships between plethysm coefficients derived
Connections between twisted Foulkes modules and symmetric functions established
Enhanced understanding of composition multiplicities in symmetric group representations
Abstract
We consider the plethysm problem stated for representations of symmetric groups. In particular, we prove new relationships between composition multiplicities of twisted Foulkes modules. Expressed in terms of symmetric functions, our results establish relationships between plethysm coefficients.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Finite Group Theory Research