List questions from symmetric-groups

Published on 08 Dec 2017 - 19:05

72

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$(12 \cdots n)$ in $S_n$ has $n-1$ inversions. What about the k-th composition?

Published on 09 Dec 2017 - 14:29

1.9k

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Show that $(1,2),(2,3),...(n-1,n)$ generate $S_n$

Published on 12 Dec 2017 - 4:31

185

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Understanding $1$-line proof that if $V$ is irreducible $\mathbb{C}S_n$-module, then $\operatorname{res}_{S_{n-1}}V$ is multiplicity free?

Published on 13 Dec 2017 - 9:08

55

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What are representative matrices of point groups (or of symmetry operations in a molecule) used for?

Published on 13 Dec 2017 - 10:18

26

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Branching graph of $\mathbb{C}S_{n}$, if $T$ is path $V_T=W_0\to W_1\to\cdots\to W_n$, why does $\mathbb{C}S_k\cdot V_T=W_k$?

Published on 15 Dec 2017 - 3:20

73

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Two Specht modules with the same composition factors.

Published on 16 Dec 2017 - 15:48

75

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If $\lambda$ is a weight of an irreducible $\mathbb{C}S_n$-module, and $\lambda_{i+1}=\lambda_i\pm 1$, then $\mu=s_i\lambda$ is not a weight?

Published on 17 Dec 2017 - 6:27

39

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Why is such a $G$ compact ?

Published on 02 Apr 2026 - 13:57

95

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Dimension of a representation of $S_n$

Published on 18 Dec 2017 - 12:16

60

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Properties of f(x) when $Gal(K/Q) ≃ S4.

Published on 19 Dec 2017 - 2:06

67

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Find all $\tau$ in $S_4$ such that $\tau (12)(34) \tau^{-1} = (12)(34)$

Published on 20 Dec 2017 - 22:21

142

Views

Character of irrep. of symmetric group.

Published on 29 Mar 2026 - 9:11

1k

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Number of fixed vectors in group action

Published on 25 Dec 2017 - 11:04

46

Views

Is $G_i$ normal in $G_k$?

Published on 29 Dec 2017 - 16:42

List Question

Action of symmetric group

$(12 \cdots n)$ in $S_n$ has $n-1$ inversions. What about the k-th composition?

Show that $(1,2),(2,3),...(n-1,n)$ generate $S_n$

Understanding $1$-line proof that if $V$ is irreducible $\mathbb{C}S_n$-module, then $\operatorname{res}_{S_{n-1}}V$ is multiplicity free?

What are representative matrices of point groups (or of symmetry operations in a molecule) used for?

Branching graph of $\mathbb{C}S_{n}$, if $T$ is path $V_T=W_0\to W_1\to\cdots\to W_n$, why does $\mathbb{C}S_k\cdot V_T=W_k$?

Two Specht modules with the same composition factors.

If $\lambda$ is a weight of an irreducible $\mathbb{C}S_n$-module, and $\lambda_{i+1}=\lambda_i\pm 1$, then $\mu=s_i\lambda$ is not a weight?

Why is such a $G$ compact ?

Dimension of a representation of $S_n$

Properties of f(x) when $Gal(K/Q) ≃ S4.

Find all $\tau$ in $S_4$ such that $\tau (12)(34) \tau^{-1} = (12)(34)$

Character of irrep. of symmetric group.

Number of fixed vectors in group action

Is $G_i$ normal in $G_k$?

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