Timeline for What is a (generalized) BN-pair?
Current License: CC BY-SA 3.0
8 events
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| Jun 28, 2012 at 7:25 | comment | added | Marc Palm | @Bugs Bunny: This was certainly a mistake. You precisely have to change the set of generators for the Coxeter group because of that fact. | |
| Jun 28, 2012 at 7:21 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Jun 27, 2012 at 15:23 | comment | added | Bugs Bunny | I am not sure what your magic $Z(F)$ is, doc, but I am quite sure that $Z(GL)\cdot SL$ is strictly smaller than $GL$. The determinant of a matrix in the former is always an $n$-th power!! In fact, the (Iwahori,Monomonial) define a BN-pair on this group, but not on the whole $GL$ | |
| Jun 27, 2012 at 14:35 | comment | added | Max Horn | Note that the center of a group with BN-pair always acts trivially on the associated building. So in a sense, the building theoretic part (and hence the BN-pair) only ``sees'' the original group modulo its center. So this "cheap trick" indeed seems quite sensible, I guess... Well, depending on what exactly you want to do ;). | |
| Jun 27, 2012 at 13:10 | comment | added | Marc Palm | Note that you will have to change the set of generators for the affine Weyl group a little bit while changing form $GL(2)$ to $SL(2)$. | |
| Jun 27, 2012 at 13:02 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Jun 27, 2012 at 12:54 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Jun 27, 2012 at 12:45 | history | answered | Marc Palm | CC BY-SA 3.0 |