# Tagged Questions

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### Highest weights of irreducible components of tensor product of irreducible sl(3)-module.

I am study the representation theory of $sl(3)$ and I have a question about the tensor representation of irreducible $sl(3)$-modules as follows: For each weight $\mu$, let $L(\mu)$ be the irreducible ...
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### Show the $\mathbb{C} S_3$-module of dimension 2 has $S(V \otimes V)$ is not irreducible

Consider the $\mathbb{C} S_3$-module of dimension 2, call it $V$. I want to concretely show that $S(V \otimes V)$ is not irreducible. I found a representation for $S_3$ over $\mathbb{C}$ of degree ...
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### properties of Sym^2 vector subspace/properties of tensor products

I have a problem: Let $V$ be an $n$-dimensional complex vector space and let $B=\{e_1,e_2,...,e_n\}$ denote the elements of a chosen basis. Let $\rho:G \to GL(V)$ be an irreducible representation. Let ...
I have a problem: Let $V$ be an $n$-dimensional complex vector space and let $B=\{e_1,e_2,...,e_n\}$ denote the elements of a chosen basis. Let $\rho:G \to GL(V)$ be an irreducible representation. Let ...