All Questions
Tagged with young-tableaux finite-groups
10
questions
1
vote
0
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44
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Normalizer of a Young subgroup in symmetric group
In $S_n$, a Young subgroup $S_{r_1}^{m_1}\times S_{r_2}^{m_2}\times ... S_{r_k}^{m_k}$ where $m_1\times r_1+...+m_k\times r_k=n$ has normalizer $N=S_{r_1}wr S_{m_1} \times ...\times S_{r_k}wr S_{m_k}$....
- 1,303
3
votes
0
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84
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Schur functors applied to irreducible representations of $S_n$
For a $d$-box Young diagram $\lambda$, the Schur functor is a functor $S_\lambda: \text{Vect}\rightarrow \text{Vect}$. If $\lambda = d$ then $S_\lambda V=S^d V$ the $d$-th symmetric power of $V$, ...
- 479
1
vote
0
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21
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Scalars by which symmetrizations of cyclic permutations act on Specht modules
Let $S_n$ be the symmetric group. Pick $a \in 2,\ldots,n$ and denote by $c_a \in \mathbb{C}[S_n]$ the symmetrization of the element $(12\ldots a)$ i.e. $c_a$ is the sum of cycles of type $a$.
Let $\...
- 135
2
votes
1
answer
80
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Weyl constructions for finite groups
Let $G$ be a finite group.
Is there a complex finite dimensional irreducible representation $V$ such that all irreducible ones are submodules of $V^{\otimes n}$ for some $n \in \mathbb{N}$?
If not, ...
- 1,822
2
votes
1
answer
288
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Why is the Young symmetrizer non-zero?
Suppose $\lambda$ is a partition of the natural number $n$ and $T$ is a standard Young Tableaux of shape $\lambda$. Let $$P_{\lambda}:=\lbrace g\in S_n:g\text{ preserves the rows of }T\rbrace$$ and $$...
- 787
0
votes
1
answer
58
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Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$
I just computed the Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$. It would be nice if anyone could confirm it's correctness. Thanks.
- 559
3
votes
0
answers
364
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Young tableaux to Specht polynomial to Irreducible representation for $(1,3,5) \in S_5$
What I am trying to do?
Work out the irreducible representation of the group element $(1,3,5) \in S_5$ for the partition $2+2+1$ .
Motivation:
Learn how to calculate irreducible representation from ...
- 559
2
votes
1
answer
384
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Representation from Young tabloids
I am following the note Young Tableaux and the Representations
of the Symmetric Group to work out a representation from a Young tableau for $S_n$.
Here $\lambda$ is a partition of an integer $n$. In ...
- 559
2
votes
1
answer
93
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Confusing partitions of $S_5$ in two different sources
I am trying to understand the partitions of $S_5$ created by it's conjugacy classes but two sources have two different partitions.
Source 1:
Source 2:
So, for example, in the first table, the ...
- 559
3
votes
2
answers
2k
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Young diagram for $S_5$
I am trying to draw the Young diagram for $S_5$. I know the following pieces of information about $S_5$.
The order of the group is $120$.
The number of conjugacy classes and so partitions is $7$.
...
- 559