Year: 2014
Type: article
Abstract: We determine the group of linear transformations preserving a polynomial function $f$ on a vector space $V$ for several interesting pairs $(V,f)$ by introducing a subgroup $G$ of $\mathrm {GL}(V)$ and applying the theory of semisimple algebraic groups. Along the way, we give an explicit description of the normalizer $N_{\mathrm {GL}(V)}(G)$ and prove that, under a mild technical assumption, the normalizer agrees with the stabilizer in $\mathrm {GL}(V)$ of the orbit of the highest weight vector in $\mathbb {P}(V)$.
Authors: H. Bermudez, S. Garibaldi, V. Larsen
Institution: Emory University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2014566716