Timeline for Decompose $\Lambda^3(V \otimes W)$ [closed]

Current License: CC BY-SA 3.0

15 events

when toggle format	what		by	license	comment
Dec 4, 2015 at 16:19	vote	accept	Jianrong Li
Dec 3, 2015 at 18:04	review	Reopen votes
Dec 3, 2015 at 21:14
Dec 3, 2015 at 16:45	history	closed	Vladimir Dotsenko Stefan Waldmann abx Marco Golla Karl Schwede		Not suitable for this site
Dec 3, 2015 at 10:32	answer	added	asv		timeline score: 2
Dec 3, 2015 at 9:46	comment	added	Robert Bryant		A stronger hint: For any vector space $V$ of dimension $n$, the kernel of the natural map $V\otimes S^2(V)\to S^3(V)$ is an irreducible $\mathrm{GL}(V)$-module of dimension $n(n-1)(n+1)/3$, and your $W_1$ must be a sum of tensor products of $\mathrm{GL}(V)$-modules with $\mathrm{GL}(W)$-modules.
Dec 3, 2015 at 9:21	comment	added	Jianrong Li		@Daniel Litt, corrected.
Dec 3, 2015 at 9:21	history	edited	Jianrong Li	CC BY-SA 3.0	added 8 characters in body
Dec 3, 2015 at 7:51	review	Close votes
Dec 3, 2015 at 16:45
Dec 3, 2015 at 7:30	comment	added	Daniel Litt		Your first formula cannot be right, since $W$ does not appear on the right hand side.
Dec 3, 2015 at 7:15	comment	added	Sh.M1972		It seems that your question is very related to the notion of "symmetry classes of tensors", you can see "Multilinear algebra" by R. Merris, where there are many similar decomposition for symmetry classes.
Dec 3, 2015 at 7:02	comment	added	Qiaochu Yuan		Instead of computing the dimension, you can try computing the character (that is, the trace of the action of a pair consisting of a diagonal matrix acting on $V$ and on $W$), then decompose the corresponding characters.
Dec 3, 2015 at 6:27	comment	added	Jianrong Li		@abx, thank you very much. I have added the parentheses.
Dec 3, 2015 at 6:26	history	edited	Jianrong Li	CC BY-SA 3.0	added 8 characters in body
Dec 3, 2015 at 4:53	comment	added	abx		You mixed $V$ and $W$ in such a way that your post is illegible. Please correct, and add parentheses.
Dec 3, 2015 at 4:07	history	asked	Jianrong Li	CC BY-SA 3.0