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Results tagged with symmetric-polynomials
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user 2384
10
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Diagonal invariants of the symmetric group on $k[X_1,X_2,...,X_n,Y_1,Y_2,...,Y_n]$
I finally got around to writing the promised details. I tried to make this a bit instructive, I hope you still find it useful.
First I will expand a bit on my comment above. A good reference is Stanl …
- 85.6k
5
votes
Accepted
Singular locus of zero set of elementary symmetric polynomial
Notice that the vanishing of $\frac{\partial}{\partial x_1} \sigma_{m,r}, \cdots, \frac{\partial}{\partial x_m} \sigma_{m,r}$ implies the vanishing of $\sigma_{m,r}$ since
$$\sigma_{m,r}=\frac{1}{r}\ …
- 85.6k