Linear preservers and representations with a 1-dimensional ring of invariants

Abstract

We determine the group of linear transformations on a vector space $V$ that preserve a polynomial function $f$ on $V$ for several interesting pairs $(V,f)$, using the theory of semisimple algebraic groups.

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• Geometric Aspects of Iterated Matrix Multiplication
• Non-Supersymmetric Magic Theories and Ehlers Truncations
• Orbits in Non-Supersymmetric Magic Theories
• On the dimension of the locus of determinantal hypersurfaces
• Generic stabilizers for simple algebraic groups
• Minuscule embeddings