Tagged Questions
3
votes
1answer
33 views
How to compute the weights of $\Gamma_{3,1}$ the irrep of $\mathfrak{sl}_3\Bbb C$
I am wondering about a combinatorial formula for computing the weights of the irreducible representations $\Gamma_{a,b}$ of $\mathfrak{sl}_3\Bbb C$. By $\Gamma_{a,b}$ I mean the irrep that has highest ...
1
vote
2answers
27 views
Computing eigenvalues for $\mathrm{Sym}^2(\mathrm{Sym}^3 V))$ for $V = \Bbb C^2$
Given $V = \Bbb C^2$ the standard representation of $\mathfrak{sl}_2\Bbb C$, on page 157 of Fulton and Harris's Representation Theory they state
Since $U = \mathrm{Sym}^3 V$ has eigenvalues $-3, ...
3
votes
1answer
242 views
Character of the $n^{\text{th}}$ symmetric power of the standard representation of $S_3$
So I am working out Fulton-Harris's Representation Theory text. For $S_3$, there is the standard representation $V$ which is two dimensional. That's all great and fine. Let $Sym^k(V)$ be the symmetric ...
