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Results tagged with symmetric-groups
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user 23959
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
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Matrix invariants for simultaneous conjugation by a finite subgroup of $\textrm{GL}_n$
Let $K$ be a field of characteristic 0, and consider $d$ generic $n\times n$ matrices $X_1,\ldots,X_d$ where $X_k = (x_{ijk})_{ij}$ and $ K[x_{ijk}]$ is the polynomial algebra in $n^2 \cdot d$ variabl …
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