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The syzygies of the d-th Veronese embedding of $\mathbb P(V)$ are functors ofthe complex vector space V. From a certain perspective, we show that as dgrows, their Schur functor decomposition is very rich whenever they are notzero. This is deduced from an asymptotic study of related plethysms. We alsoobtain other results related to a question of Ein and Lazarsfeld.

Asymptotic Schur decomposition of Veronese syzygy functors