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Results tagged with rt.representation-theory
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user 23980
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
vote
0
answers
277
views
Irreducible representations of $S_n$ inside the ring of symmetric polynomials
I will describe two ways to associate irreducible representations of $S_n$ with polynomials inside the ring of symmetric polynomials and I want to know if there is any connection between the two.
$\t …
- 1,305
1
vote
Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambd...
Here is a representation theoretic argument. I hope it is correct.
Consider the weight diagram of the irreducible representation $V_\lambda$ (of highest weight $\lambda$) of $\mathfrak{sl}_n(\mathbb{ …
- 1,305
5
votes
1
answer
374
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Plethysm of $S^3(S^2V)$ as $\mathfrak{sl}_3(\mathbb{C})$-module
I have asked this question in MSE before, but have not got any answer. So here I am asking it again with some more detail.
I believe that the following sequence of $\mathfrak{sl}_3(\mathbb{C})$-modul …
- 1,305
21
votes
14
answers
3k
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Applications of Representation Theory in Combinatorics
What are the examples of interesting combinatorial identities (e.g. bijection between two sets of combinatorial objects) that can be proved using representation theory, or has some representation theo …