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arXiv · 1806.04984

Slopes of Euclidean lattices, tensor product and group actions

Renaud Coulangeon·Gabriele Nebe
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Abstract

We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $μ_{min}(L \otimes M) = μ_{min}(L)μ_{min}(M)$ for all Euclidean lattices $L$ and $M$. We prove that this is the case under the additional assumptions that $L$ and $M$ are acted on multiplicity-free by their automorphism group, such that one of them has at most $2$ irreducible components.

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Renaud Coulangeon, Gabriele Nebe. 2018-11-23. Slopes of Euclidean lattices, tensor product and group actions. https://arxiv.org/abs/1806.04984

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