Plethysms of symmetric functions and highest weight representations

  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},
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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