# Plethysms of symmetric functions and highest weight representations

@article{Boeck2021PlethysmsOS, title={Plethysms of symmetric functions and highest weight representations}, author={Melanie de Boeck and Rowena Paget and Mark Wildon}, journal={Transactions of the American Mathematical Society}, year={2021} }

Let $s_\nu \circ s_\mu$ denote the plethystic product of the Schur functions $s_\nu$ and $s_\mu$. In this article we define an explicit polynomial representation corresponding to $s_\nu \circ s_\mu$ with basis indexed by certain `plethystic' semistandard tableaux. Using these representations we prove generalizations of four results on plethysms due to Bruns--Conca--Varbaro, Brion, Ikenmeyer and the authors. In particular, we give a sufficient condition for the multiplicity $\langle s_\nu \circ…

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