Timeline for Sign problem in a Calogero-Moser system: proof of integrability?
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 25, 2016 at 13:46 | vote | accept | Olga | ||
| Jan 25, 2016 at 13:46 | answer | added | Olga | timeline score: 4 | |
| Jan 22, 2016 at 10:52 | comment | added | Olga | The condition $\mathrm{rk}([X,Y]+1)=1$ should still hold and by changing non-diagonal values of $Y$ like this I think we will get out of this condition. We can change both matrices by conjugating them by some matrix from $PGL_n(\mathbb{C})$. $X$ is diagonal. We would love to get $Y_{j k}$ as you write them but this is not possible to pass from a matrix [ M= \begin{bmatrix} p_1 & \frac{1}{x_1-x_2} \\ \frac{1}{x_2-x_1} & p_2 \end{bmatrix} ] to [ M= \begin{bmatrix} p_1 & \frac{i}{x_1-x_2} \\ \frac{i}{x_2-x_1} & p_2 \end{bmatrix} ] by (even complex) conjugacy | |
| Jan 21, 2016 at 20:39 | comment | added | BS. | Hi Olga ! I think that even though the CM system is real, you can consider it coming from complex (hermitian) matrices, whose (real) eigenvalues should be the positions of the "particles". Hence it would be legit to take $Y_{jk}=\sqrt{-1}/(x_j-x_k)$... It's sometimes hard to guess something from its shadow! | |
| Jan 21, 2016 at 20:33 | history | edited | BS. | CC BY-SA 3.0 |
added 4 characters in body
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| S Jan 21, 2016 at 20:12 | history | suggested | jeq | CC BY-SA 3.0 |
Corrected typo. Modified tags.
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| Jan 21, 2016 at 19:53 | comment | added | AHusain | What's wrong with the $i*x$ change of variables? | |
| Jan 21, 2016 at 19:43 | review | Suggested edits | |||
| S Jan 21, 2016 at 20:12 | |||||
| Jan 21, 2016 at 17:40 | history | edited | Olga | CC BY-SA 3.0 |
deleted 17 characters in body
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| Jan 21, 2016 at 16:27 | history | asked | Olga | CC BY-SA 3.0 |