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}
}
• Published 2 May 2021
• Mathematics
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 ∼= SymSymmE. 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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