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On the inverse problem for isometry groups of norms

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GR2W02 - Simple groups, representations and applications

 We study the problem of determining when a compact group can be realized as the group of isometries of a norm on a finite dimensional real vector space V.  We give a geometric characterization of such groups in terms of their vector closure. Using factorizations of compact Lie groups as well as a new characterization of irreducible prehomogeneous spaces, we prove that every compact connected subgroup of linear transformations can be realized as the connected component of the identity of the isometry group of some norm on V, except for an explicit list of exceptions. (joint work with Martin Liebeck, Assaf Naor and Aluna Rizzoli)

This talk is part of the Isaac Newton Institute Seminar Series series.

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