Timeline for Irreducible representation flipping two elements
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2011 at 16:15 | comment | added | ndkrempel | Yes, that's right. | |
| Mar 9, 2011 at 15:46 | comment | added | fherzig | Thanks! I now remembered the 1969 paper of Tits solving the word problem for Coxeter groups (MR0254129). You are using his result mentioned in the MR review about when two words are equal, right? | |
| Mar 9, 2011 at 12:46 | vote | accept | Klim Efremenko | ||
| Mar 9, 2011 at 0:24 | comment | added | ndkrempel | Well, not exactly a normal form. But two words representing the same element both lead to some common word upon making a sequence of replacements of the forms $s_a s_a \mapsto 1$ and $s_a s_b s_a s_b s_a \dots \mapsto s_b s_a s_b s_a s_b \dots$. But since the words I used don't contain more than one of a given simple reflection, you can never make the first type of replacement (so in particular, they are minimum length representatives), and the second type of replacement merely changes the ordering. Hence they represent distinct elements of the Coxeter group. | |
| Mar 8, 2011 at 22:50 | comment | added | fherzig | What's the normal form you are alluding to? | |
| Mar 8, 2011 at 13:51 | history | edited | ndkrempel | CC BY-SA 2.5 |
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| Mar 8, 2011 at 13:42 | history | edited | ndkrempel | CC BY-SA 2.5 |
added 182 characters in body
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| Mar 8, 2011 at 13:34 | history | answered | ndkrempel | CC BY-SA 2.5 |