All Questions
Tagged with young-tableaux permutations
12
questions
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42
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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
1
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1
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140
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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
8
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5
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709
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What are the end and coend of Hom in Set?
A functor $F$ of the form $C^{op} \times C \to D$ may have an end $\int_c F(c, c)$ or a coend $\int^c F(c, c)$, as described for example in nLab or Categories for Programmers. I'm trying to get an ...
- 4,207
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274
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Irreducible representations of $S_5$ and their Young diagrams
Given a Young tableau, we can construct its Young symmetrizer $c_\lambda$. Then, the ideal $\mathbb{C} S_n \cdot c_\lambda$ is an irreducible representation of $S_n$. Exercise 4.5 in Fulton and Harris ...
- 172
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Number of building block structures following a set of rules
If we have an n amount of building blocks, and we are tasked with making, what I have found out are 'Young Tableau' like structures (though I am unsure if they are exactly the same), how many can we ...
3
votes
1
answer
293
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The number of permutations that can be written in two ways as a product of row and column permutations of a Young tableau
My question is related to an issue in the book "Young tableaux" by W.Fulton. Consider a Young tableau $T$ of a given fixed shape filled with integers $1,\ldots,n$. A permutation $\sigma$ in ...
2
votes
1
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405
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Characters of permutation representations for $S_4$
I am going through the lecture note How to get character tables of symmetric groups.
On page 2, it computes the character table of $S_4$. The procedure starts with building the table of the ...
- 559
3
votes
1
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460
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321-avoiding permutations and RSK
I am reading through a book on enumeration and I came across a weird statement:
Using RSK (Robinson-Schensted-Knuth Correspondence), one can show that 321-avoiding permutations are Catalan objects.
...
- 51
4
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354
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Can essentially primitive idempotents be defined both as $e_\lambda=s_\lambda a_\lambda$ and $e_\lambda=a_\lambda s_\lambda$?
I've been studying representation theory of symmetric group on Tung's Group Theory in Physics. I understood that different Young Diagrams corresponds to inequivalent irreducible representations of ...
- 243
5
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2
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397
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A question about irreducible representation of symmetric group (permutation group) in tensor space and tensor contraction
In chapter 13 of the textbook of Group Theory in Physics by Wu-Ki Tung, Lemma 2 discusses the equivalence of two irreducible representations of GL(m) on ${T^i}_j$. In its proof, it simply mentioned (...
- 243
2
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435
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I want to decompose a tensor product using Littlewood-Richardson rule, How do I find the component of this in each irreducible space?
Let me set up the notation I am using. $(abc,de)$ denotes the standard Young tableau where the first row is $abc$ and the second row is $de$. Each young tableau corresponds to the young symmetriser, ...
- 63
24
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1
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1k
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Involutions, RSK and Young Tableaux
Let $S_n$ be the symmetric group on $n$ elements. The Robinson-Schensted-Knuth (RSK) correspondence sends a permutation $\pi\in S_n$ to a pair of Standard Young Tableaux $(P,Q)$ with equal shapes $\...
- 32.9k