# Modular plethystic isomorphisms for two-dimensional linear groups

@inproceedings{McDowell2021ModularPI, title={Modular plethystic isomorphisms for two-dimensional linear groups}, author={Eoghan McDowell and Mark Wildon}, year={2021} }

Let E be the natural representation of the special linear group SL2(K) over an arbitrary field K. We use the two dual constructions of the symmetric power when K has prime characteristic to construct an explicit isomorphism SymmSym E ∼= Sym`SymmE. This generalises Hermite reciprocity to arbitrary fields. We prove a similar explicit generalisation of the classical Wronskian isomorphism, namely SymmSym E ∼= ∧m Sym`+m−1E. We also generalise a result first proved by King, by showing that if ∇ is…

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