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Omid Hatami
Omid Hatami
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This might be a classic question, but since I am new to representation theory of the symmetric group, I am asking it here.

Suppose that $n=k+l+r$ where $k,l$ are positive and $r\geq 0$$k\geq l\geq r\geq 0$. Let $G$ be the symmetric group $S_n$ and $H$ be its Young subgroup $S_k \times S_l \times S_1^r$. What can be said about the induced representation $\mbox{Ind}_H^G 1$? What are its components? Can we say something about their multiplicities?

This might be a classic question, but since I am new to representation theory of the symmetric group, I am asking it here.

Suppose that $n=k+l+r$ where $k,l$ are positive and $r\geq 0$. Let $G$ be the symmetric group $S_n$ and $H$ be its Young subgroup $S_k \times S_l \times S_1^r$. What can be said about the induced representation $\mbox{Ind}_H^G 1$? What are its components? Can we say something about their multiplicities?

This might be a classic question, but since I am new to representation theory of the symmetric group, I am asking it here.

Suppose that $n=k+l+r$ where $k\geq l\geq r\geq 0$. Let $G$ be the symmetric group $S_n$ and $H$ be its Young subgroup $S_k \times S_l \times S_1^r$. What can be said about the induced representation $\mbox{Ind}_H^G 1$? What are its components? Can we say something about their multiplicities?

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Omid Hatami
Omid Hatami
  • 901
  • 5
  • 19

Induced representation of a Young subgroup

This might be a classic question, but since I am new to representation theory of the symmetric group, I am asking it here.

Suppose that $n=k+l+r$ where $k,l$ are positive and $r\geq 0$. Let $G$ be the symmetric group $S_n$ and $H$ be its Young subgroup $S_k \times S_l \times S_1^r$. What can be said about the induced representation $\mbox{Ind}_H^G 1$? What are its components? Can we say something about their multiplicities?