Timeline for Equivalence of exterior forms
Current License: CC BY-SA 3.0
5 events
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| Jun 23, 2014 at 14:10 | comment | added | Robert Bryant | @tatin: Sure. Intuitively, the reason for this result is that there can't be open orbits of $\mathrm{GL}(n,\mathbb{R})$ on $\Lambda^k(\mathbb{R}^n)$ unless $n^2\ge {n\choose k}$. Amazingly, this one necessary inequality turns out to be sufficient to imply that there actually is an open orbit except in the trivial case $k=0$ (in which case, the action of $\mathrm{GL}(n,\mathbb{R})$ is trivial). The above list is just the list of cases in which the inequality holds, and it turns out that, when there is at least one open orbit, then there is only a finite number of orbits all told. | |
| Jun 23, 2014 at 13:57 | comment | added | Tatin | @Bryant: Thank you very much for your answer. I'm very suprized by the result. Could you please suggest me a reference where I can find proofs on why we have continuous moduli in all other cases. Intuitively, is it possible to explain the existence of exceptional cases. | |
| Jun 23, 2014 at 13:52 | vote | accept | Tatin | ||
| Jun 23, 2014 at 13:21 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Expanded on the information provided for the benefit of the reader
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| Jun 22, 2014 at 18:53 | history | answered | Robert Bryant | CC BY-SA 3.0 |