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Tagged with young-tableaux irreducible-representation
3
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Restriction of induced representation over a Young subgroup and Littlewood-Richardson coefficients
I'm inexperienced in the representation theory of the symmetric group, so please correct my possible mistakes. Fix $m\leq n$, $G:=S_n$ and $H:=S_m\times S_{n-m}$ as a Young subgroup of $G$. Let $V^{\...
- 4,886
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Tableau which corresponds to alternating square representation
Recall that $S_5$ acts on $\mathbb C^5$ by permuting its coordinates and that $\mathbb C^5$ decomposes as $V\oplus W$ where $W$ is the trivial representation and $V$ has dimension $4$. Show that the ...
- 9,592
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The irreducible representation of $S_n$ corresponding to the partition $n = (n − 1) + 1$
Let a finite group $G$ act doubly transitively on a finite set $X$, i.e., given $x,y,z,w\in X$ such that $x\neq y$ and $z\neq w$, there is a $g\in G$ such that $g.x=z$ and $g.y=w$. So, we can write
$$\...
- 9,592