Timeline for For a representation V of a finite group G, when is Hom(W, W⊗V) trivial for all irreps W?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2010 at 4:19 | vote | accept | Qiaochu Yuan | ||
| Apr 25, 2010 at 22:57 | answer | added | pasquale zito | timeline score: 2 | |
| Apr 25, 2010 at 22:22 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
Unicode fix for the title
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| Apr 25, 2010 at 21:53 | answer | added | Dylan Thurston | timeline score: 5 | |
| Apr 25, 2010 at 21:25 | comment | added | Qiaochu Yuan | To be more precise: yes, I know this, but it says nothing about how the representations [n], [n-1], [n+1] decompose as representations of G. | |
| Apr 25, 2010 at 20:46 | answer | added | Theo Johnson-Freyd | timeline score: 1 | |
| Apr 25, 2010 at 20:41 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
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| Apr 25, 2010 at 20:27 | comment | added | Theo Johnson-Freyd | If you know the representation theory of $\rm SU(2)$, the fact that $\hom(W,W\otimes V) = 0$ is immediate for $W$ a finite-dimensional irrep. Indeed, remember that the finite-dimensional irreps of $\rm SU(2)$ are classified by their dimension — there is one for each positive integer — and we have the decomposition $[n] \otimes 2 = [n-1] \oplus[n+1]$. But I assume that you know this line of reasoning, and are either trying to prove the representation theory or are simply interested in the more general case. | |
| Apr 25, 2010 at 20:27 | answer | added | Ben Webster♦ | timeline score: 13 | |
| Apr 25, 2010 at 20:16 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
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| Apr 25, 2010 at 19:53 | history | asked | Qiaochu Yuan | CC BY-SA 2.5 |