Similarly one can express elementary symmetric polynomials via traces over antisymmetric tensor powers.
2.
The set of elementary symmetric polynomials in variables ring of symmetric polynomials in variables.
3.
For example, the stabilizer of an elementary symmetric polynomial is the whole group.
4.
From this point of view the elementary symmetric polynomials are the most fundamental symmetric polynomials.
5.
For more information on this subject, see elementary symmetric polynomial and Viete's formulas.
6.
(this is actually an identity of polynomials in, because after the elementary symmetric polynomials become zero ).
7.
These are power sums and you can use Newton's identities to convert these into elementary symmetric polynomials.
8.
As mentioned, Newton's identities can be used to recursively express elementary symmetric polynomials in terms of power sums.
9.
That is, any symmetric polynomial is given by an expression involving only additions and multiplication of constants and elementary symmetric polynomials.
10.
Thus, for each positive integer less than or equal to there exists exactly one elementary symmetric polynomial of degree in variables.
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