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15 votes
2 answers
838 views

factorization of the regular representation of the symmetric group

Let $\mathbb{C}[S_n]$ be the regular representation of the symmetric group $S_n$, and let $\mathbb{C}^n$ be the vector representation. Question: Does there exist a representation $V$ (of dimension $(...
Nicholas Proudfoot's user avatar
2 votes
0 answers
184 views

The canonical automorphism of the symmetric group

Let $S_n$ be the symmetric group of order $n$. Denoting simple transpositions by $\sigma_i$ the collection $\sigma_1, \dots, \sigma_{n-1}$ generates $S_n$ subject to the following relations: $$ \sigma ...
Jake Wetlock's user avatar
  • 1,144
-2 votes
2 answers
734 views

Lie algabra of symmetric group

It's easy to see that the descending central series of a group induces a graded Lie algebra .(see for example Serre's Harvard lectures or Magnus-Solitar book). I think in general this can be ...
Dr Shello's user avatar
  • 1,180