Timeline for Reference Request: Length of a reflection in a Coxeter group can be achieved by symmetric word
Current License: CC BY-SA 4.0
9 events
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| Nov 4, 2018 at 23:40 | history | edited | Matt Samuel | CC BY-SA 4.0 |
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| Nov 4, 2018 at 17:32 | comment | added | Matt Samuel | @oui I finished the proof for completeness. It doesn't use symmetry of the word. | |
| Nov 4, 2018 at 17:31 | history | edited | Matt Samuel | CC BY-SA 4.0 |
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| Nov 4, 2018 at 16:30 | comment | added | ouimerci | Well, I think this answers my question then! | |
| Nov 4, 2018 at 16:29 | vote | accept | ouimerci | ||
| Nov 4, 2018 at 16:24 | comment | added | Matt Samuel | @ouimerci That's right, I prove that such a word exists. | |
| Nov 4, 2018 at 16:23 | comment | added | ouimerci | So, you're showing that for any root $\beta$, $s_\beta$ can be written with a symmetric word of length $2\mathrm{dp}(\beta) -1$, right? Then, to answer the question/claim in my post, you'd essentially combine that with the equality written there. I'm not sure of what you assume and what you conclude. (And thanks!) | |
| Nov 4, 2018 at 15:20 | history | edited | Matt Samuel | CC BY-SA 4.0 |
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| Nov 4, 2018 at 15:03 | history | answered | Matt Samuel | CC BY-SA 4.0 |