All Questions
Tagged with young-tableaux direct-sum
3
questions
1
vote
1
answer
1k
views
$8 \otimes 8$ in $SU(3)$, dimension of the Young-tableau corresponding to the $\bar{10}$
In Georgi's Lie Algebras in Particle Physics, he calculates the decomposition of $8\otimes 8$ in $SU(3)$, and obtains
$$8\otimes 8 = 27 \oplus 10 \oplus \bar{10} \oplus 8 \oplus 8 \oplus 1,$$
...
- 157
2
votes
1
answer
213
views
Do we have $\mathbb{C}[\text{SL}_n] = \bigoplus_{\lambda, \,\text{ht}(\lambda)\leq n} V_{\lambda} $?
The coordinate algebra $$\mathbb{C}[\text{SL}_n]=\mathbb{C}\big[x_{ij}: i, j \in \{1, \ldots, n\}\big]/\big(\det(x_{ij}) - 1\big)$$ is a representation of $\text{SL}_n$: $$(g'.f)(g)=f(g'^T g)\,.$$
Let ...
- 14.6k
1
vote
0
answers
114
views
Simplifying a direct sum $\mathbf{3}\oplus\mathbf{3}\oplus\mathbf{2}$ etc
In particle physics, one often uses the dimensionality of the irrep to label the irrep (apparently this is not a very good idea since the dimension does not unambiguously determine the rep.). What are ...
- 719