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Results tagged with invariant-theory
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user 4008
Invariant theory deals with an algebraic, geometric or analytic structure $X$, submitted to the action of an (algebraic) group $G$. It studies $G$-invariant elements of $X$ as well as the set of $G$-orbits.
21
votes
Accepted
Chevalley–Shephard–Todd theorem
There are indeed many presentations (if I remember correctly Bourbaki has it)
but the proof is very elegant and short so that I find it hard to refrain from giving
it. Let $H$ be the normal subgroup o …
- 22.6k
20
votes
Accepted
Is $Sym^n (V^*) \cong Sym^n (V)^\ast$ naturally in positive characteristic?
The answer is no (and well-known to people working in the representation theory of algebraic groups in positive characteristic). In fact for $V$ finite dimensional and of dimension $>1$ the two vector …
- 22.6k
6
votes
On the field of invariants of a finite group
It seems likely (and may be known) that it does depend on the permutation representation. However, it is a subtle question as the stable isomorphism class (of any faithful permutation, or in fact arbi …
- 22.6k