All Questions
Tagged with young-tableaux exterior-algebra
3
questions
3
votes
0
answers
84
views
Schur functors applied to irreducible representations of $S_n$
For a $d$-box Young diagram $\lambda$, the Schur functor is a functor $S_\lambda: \text{Vect}\rightarrow \text{Vect}$. If $\lambda = d$ then $S_\lambda V=S^d V$ the $d$-th symmetric power of $V$, ...
- 479
3
votes
1
answer
184
views
Antisymmetric tensors of a tensor product: $\Lambda^k(V \otimes W)$
Given two vector spaces $V, W$ over $\mathbb{R}$, it's true that
$\Lambda^2 (V \otimes W) \cong \left(\Lambda^2 V \otimes S^2 W \right) \oplus \left( S^2 V \otimes \Lambda^2 W \right)$. If I'm seeing ...
- 1,663
14
votes
2
answers
2k
views
Young diagram for exterior powers of standard representation of $S_{n}$
I'm trying to solve ex. 4.6 in Fulton and Harris' book "Representation Theory". It asks about the Young diagram associated to the standard representation of $S_{n}$ and of its exterior powers. The ...
- 4,374