The Stabilizer of Elementary Symmetric Polynomials
  We study the r-th elementary symmetric polynomial in $n$ variables with 2<r<n. There are two kinds of linear transformations on the parameter space that leave this polynomial invariant: Namely, any permutation of the variables and simultaneous scaling by any r-th root of unity. We prove that there are no other linear transformations with this property. 
Jesko H\"uttenhain
math.AC math.RA