Timeline for Basics of classification of trilinear forms (when is it non-discrete)
Current License: CC BY-SA 4.0
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| Jun 1 at 18:12 | history | edited | Steven Sam | CC BY-SA 4.0 |
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| Feb 11, 2013 at 3:04 | comment | added | Steven Sam | For an explicit example from the paper: consider the action of $SL_6 \times GL_{19}$ on $\bigwedge^3 \mathbf{C}^6 \otimes \mathbf{C}^{19}$. | |
| Feb 11, 2013 at 3:03 | comment | added | Steven Sam | Possible reference is Kac's paper "Some remarks on nilpotent orbits" which cites other papers: ams.org/mathscinet-getitem?mr=575790 (but note that $2 \times 2 \times n$ is treated as $4$-dimensional orthogonal space tensored with $n$-dimensional space as I wrote it). If a representation has a dense open orbit, it does NOT imply finitely many orbits. These are called prehomogeneous vector spaces. The irreducible ones were studied by Sato-Kimura: ams.org/mathscinet-getitem?mr=430336 Examples of infinitely many orbits is on p.150. | |
| Feb 10, 2013 at 20:08 | comment | added | Dmitry Kerner | Thanks! Still more questions: 1. Where is this written? (Instead of writing down the reasoning in my paper I'd prefer just to cite some text) 2. Suppose, for a given group acting on a space, there is just one open dense orbit. Does it imply that all the orbits are discrete (no moduli)? I cannot think of any counterexample, being ignorant. Or, maybe there are some additional (not too restrictive) conditions ? | |
| Feb 10, 2013 at 20:04 | vote | accept | Dmitry Kerner | ||
| Feb 10, 2013 at 19:03 | history | edited | Steven Sam | CC BY-SA 3.0 |
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| Feb 10, 2013 at 18:50 | history | edited | Steven Sam | CC BY-SA 3.0 |
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| Feb 10, 2013 at 18:44 | history | answered | Steven Sam | CC BY-SA 3.0 |