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Slopes of Euclidean lattices, tensor product and group actions

  • Renaud CoulangeonEmail author
  • Gabriele Nebe
Article
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Abstract

We study the behavior of the minimal slope of Euclidean lattices (or more generally Ok-lattices) under tensor product. A general conjecture predicts that
$${\mu _{\min }}\left( {L \otimes M} \right) = {\mu _{\min }}\left( L \right){\mu _{\min }}\left( M \right)$$
for all 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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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de BordeauxUniversité de Bordeaux CNRS, IMB, UMR 5251Talence cedexFrance
  2. 2.Lehrstuhl D für MathematikRWTH AachenAachenGermany

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