Timeline for Known decomposition of $\bigwedge^k Sym^d \mathbb C^n$ in special cases?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2013 at 17:51 | vote | accept | stepanp21 | ||
| Feb 15, 2013 at 10:28 | comment | added | Mark Wildon | Thank you for the reference. As you say in your paper, it's a remarkable isomorphism. | |
| Feb 14, 2013 at 14:32 | comment | added | Abdelmalek Abdesselam | ...the page 43 is the first of the article. The one where this isomorphism is mentioned is page 46. | |
| Feb 14, 2013 at 14:17 | comment | added | Abdelmalek Abdesselam | @Mark: that symmetric plethysm is isomorphic to wedge^{k} sym^{d+k-1} via the so-called Wronskian isomorphism. See my paper with Chipalkatti in J. Pure App. Algebra vol. 210 p. 43. This is why the Cayley-Sylvester formula gives the answer for that case too. | |
| Feb 14, 2013 at 4:45 | comment | added | Mark Wildon | When $n=2$ the plethysm ${\rm Sym^k}{\rm Sym^d}V$ is given by the Cayley-Sylvester formula. I can't see why this is equivalent to knowing your plethysm. But I think it should be possible to work out the constituents of $\bigwedge^k ({\rm Sym}^d V)$ using similar arguments with formal characters of ${\rm SL_2}(\mathbb{C})$. | |
| Feb 14, 2013 at 4:39 | answer | added | Mark Wildon | timeline score: 8 | |
| Feb 13, 2013 at 22:39 | history | asked | stepanp21 | CC BY-SA 3.0 |