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3 questions
15
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2
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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 $(...
2
votes
0
answers
184
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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 ...
-2
votes
2
answers
734
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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 ...