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Results tagged with symmetric-polynomials
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user 1306
4
votes
Isotypic components of the action of the symmetric group on polynomials
The answer depends on the structure that you want on the collection of generators you are looking for. If you really want just generators of $\mathbb{C}[x_1,\ldots,x_n]$ over $\mathbb{C}[x_1,\ldots,x_ …
- 16.9k
4
votes
Accepted
A nice generating set for the symmetric power of an algebra
Since your algebra is finitely generated, you only really need this result in the case when $A=\mathbb{C}[t_1,\ldots,t_n]$.
It seems that this result first appeared in
F. Junker, Über symmetrische …
- 16.9k
7
votes
Accepted
Generalizing the Fundamental Theorem of Symmetric Polynomials
I heard of three relatively recent works in that direction, taking different routes and arriving to interesting information about diagonal invariants.
First, there is the paper of Vaccarino that Dar …
- 16.9k
3
votes
Accepted
Alternating elements in free graded-commutative algebras
If you assume $\ell>n$, then you may as well work over the field $F=\mathbb{Q}$, since the representation theory is exactly the same (the group algebra is semisimple, all Young symmetrisers in the gro …
- 16.9k
7
votes
Applying $\sum_i \partial_{x_i}$, $\sum_i x_i \partial_{x_i}$ and $\sum_i x_i^2 \partial_{x_...
The answer for $L_1=\sum_ix_i^2\partial_i$ can be derived in a rather straightforward way (I changed your convention a little bit to match the usual formulas for Virasoro algebra). Namely, use the det …
- 16.9k