Slopes of Euclidean lattices, tensor product and group actions

Renaud Coulangeon; Gabriele Nebe

Slopes of Euclidean lattices, tensor product and group actions

Number Theory 2018-11-26 v2

Authors: Renaud Coulangeon , Gabriele Nebe

Abstract

We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $\mu_{min}(L \otimes M) = \mu_{min}(L)\mu_{min}(M)$ 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.

Keywords

Euclidean lattices minimal slope tensor product automorphism group multiplicity-free irreducible components

Cite

@article{arxiv.1806.04984,
  title  = {Slopes of Euclidean lattices, tensor product and group actions},
  author = {Renaud Coulangeon and Gabriele Nebe},
  journal= {arXiv preprint arXiv:1806.04984},
  year   = {2018}
}

Comments

Update of a previous version. The main result is now stated for Hermitian bundles over totally real or CM number fields. A few proofs of intermediate results have been simplified

Slopes of Euclidean lattices, tensor product and group actions

Abstract

Keywords

Cite

Comments

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