Corpus ID: 233481226

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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