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SIMPLE GROUPS STABILIZING POLYNOMIALS

2015
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Forum of Mathematics, Pi
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We study the problem of determining, for a polynomial function$f$on a vector space$V$, the linear transformations$g$of$V$such that$f\circ g=f$. When$f$is invariant under a simple algebraic group$G$acting irreducibly on$V$, we note that the subgroup of$\text{GL}(V)$stabilizing$f$often has identity component$G$, and we give applications realizing various groups, including the largest exceptional group$E_{8}$, as automorphism groups of polynomials and algebras. We show that, starting with a simple

doi:10.1017/fmp.2015.3
fatcat:3jwmr5rkgnfyllpgaqvnozbexa