The complexity of the Lie module

Mathematics – Representation Theory

Scientific paper

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Scientific paper

We show that the complexity of the Lie module $\mathrm{Lie}(n)$ in
characteristic $p$ is bounded above by $m$ where $p^m$ is the largest $p$-power
dividing $n$ and, if $n$ is not a $p$-power, is equal to the maximum of the
complexities of $\Lie(p^i)$ for $1 \leq i \leq m$.

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