## New answers tagged symmetric-functions

3
votes

### Matrix invariants for simultaneous conjugation by a finite subgroup of $\textrm{GL}_n$

Just a complement to Igor's very nice answer.
Indeed, Weyl is often credited with the FFTs of classical invariant theory for various groups, but the latter were known and rigorously proven before. ...

6
votes

Accepted

### Matrix invariants for simultaneous conjugation by a finite subgroup of $\textrm{GL}_n$

I believe that all these results are applications of the so called First Fundamental Theorem (FFT) of Invariant Theory of $G$, where $G$ is a specific group, which in your case is either $\mathrm{GL}...

1
vote

Accepted

### Dense subspace of space of radial functions in $H^1_0(\Omega)$

The inclusion $\overline{C^\infty_{0,\text{rad}}(\Omega)}^{H^1_0(\Omega)} \subset H^1_{0,\text{rad}}(\Omega)$ is trivial.
For the reverse inclusion take $u \in H^1_{0,\text{rad}}(\Omega)$ and observe ...

6
votes

Accepted

### Poisson kernel for the orthogonal groups

The Poisson kernel for the orthogonal group was calculated by Benjamin Béri in Generalization of the Poisson kernel to the superconducting random-matrix ensembles. This is in the context where $X$ is ...

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