Timeline for Why is there such a close resemblance between the unitary representation theory of the Virasoro algebra and that of the Temperley-Lieb algebra?
Current License: CC BY-SA 3.0
23 events
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| S Feb 14, 2014 at 20:06 | history | suggested | Sebastien Palcoux | CC BY-SA 3.0 |
Several minor edits.
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| Feb 14, 2014 at 19:39 | review | Suggested edits | |||
| S Feb 14, 2014 at 20:06 | |||||
| Oct 14, 2013 at 20:42 | vote | accept | André Henriques | ||
| S Oct 11, 2013 at 13:25 | history | suggested | Sebastien Palcoux | CC BY-SA 3.0 |
I have improved the shape of the table and of some lists. I have added the tag "subfactors".
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| Oct 11, 2013 at 13:19 | review | Suggested edits | |||
| S Oct 11, 2013 at 13:25 | |||||
| Oct 11, 2013 at 13:18 | answer | added | Sebastien Palcoux | timeline score: 16 | |
| Jul 20, 2011 at 19:14 | comment | added | André Henriques | Thank you Marcel for the link. I think that I now understand the general picture. | |
| Jul 20, 2011 at 18:49 | comment | added | Marcel Bischoff | Btw on wikipedia the example is discussed en.wikipedia.org/wiki/Finite_potential_well and it is actually not so simple to calculate the discrete eigenvalues because there is no closed solution. @Theo in your Hamiltonian is missing a square for $(-i\frac\partial{\partial x})$ | |
| Jul 20, 2011 at 1:25 | comment | added | Theo Johnson-Freyd | @André: Yes, I meant for $V$ to be bounded, not just bounded below. I rewrote my comment a few times, and somehow that got lost. Marcel's example is spot on, even if it doesn't quite satisfy my fairly restrictive conditions. | |
| Jul 19, 2011 at 11:44 | history | edited | André Henriques | CC BY-SA 3.0 |
added 178 characters in body
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| Jul 18, 2011 at 16:01 | comment | added | Marek | @André, something like this: etsf.eu/system/files/born-oppenheimer-m.png -- as one gets closer to the "top of the well" the energy levels are getting finer and eventually they become continuous (it depends on the precise profile whether there is a finite or infinite number of the discrete levels though). I am not sure what is the picture of but qualitatively it resembles the radial part of a Coulomb potential (as felt e.g. by an electron orbiting a nucleus). | |
| Jul 18, 2011 at 15:34 | answer | added | Eric Rowell | timeline score: 5 | |
| Jul 18, 2011 at 13:00 | comment | added | Marcel Bischoff | ok maybe not a good example because it has finite discrete spectrum... | |
| Jul 18, 2011 at 12:54 | comment | added | Marcel Bischoff | The simplest examples of what Theo is talking about is probably $V(x) = -1_{[-1,1]}(x)$ the negative characteristic function of an interval. For energy $-1< E<0$ the spectrum of the Hamiltonian is discrete for $E>0$ continuous. | |
| Jul 18, 2011 at 12:36 | comment | added | André Henriques | @Theo: In your example, is V(x) is a bounded function? (if not: what do you mean by "top of the mountains"?). What is the simplest example of a function V(x) that exhibits the kind of behavior that you describe? | |
| Jul 18, 2011 at 11:40 | comment | added | Theo Johnson-Freyd | Maybe Qiaochu's question is the following. As physicists, we're very used to the following phenomenon: let $V(x)$ be a potential energy function which bounded below and has finitely many local minima (I probably can relax something). Then the spectrum of the Hamiltonian $(i\hbar\frac{\partial}{\partial x}) + V(x)$ has a discrete part, roughly corresponding to valleys in the graph of $V$, and a continuous part, starting near the tops of the mountains and going higher. Here the role of $c,\delta$ is played by the energy $E$ = eigenvalue. So your remarked upon behavior is not a priori surprising. | |
| Jul 18, 2011 at 1:37 | answer | added | Stephen | timeline score: 15 | |
| Jul 18, 2011 at 1:15 | history | edited | André Henriques | CC BY-SA 3.0 |
added the positive energy constraint. Without it, the stated facts about Rep(Vir_c) aren't correct.; added 70 characters in body; deleted 4 characters in body
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| Jul 18, 2011 at 0:27 | history | edited | André Henriques | CC BY-SA 3.0 |
edited title
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| Jul 18, 2011 at 0:27 | comment | added | André Henriques | @Qiaochu: What do you mean by "objects of this type"? | |
| Jul 17, 2011 at 23:55 | comment | added | Qiaochu Yuan | Is it clear that this isn't the generic expected behavior for objects of this type? | |
| Jul 17, 2011 at 23:12 | history | edited | André Henriques | CC BY-SA 3.0 |
edited title
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| Jul 17, 2011 at 22:28 | history | asked | André Henriques | CC BY-SA 3.0 |
