Timeline for Cohomology ring of BG
Current License: CC BY-SA 3.0
3 events
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| Dec 20, 2012 at 20:23 | comment | added | Craig Westerland | Oh, maybe this is nonsense -- the 0 dimensional class is the trivial factor in the regular representation, and the 2 dimensional factor is the reduced regular representation. What is subtle here is that how the regular representation knows which summands correspond to which cohomological degrees. I suppose that this should be related to the Bruhat order on the Weyl group. | |
| Dec 20, 2012 at 20:16 | comment | added | Craig Westerland | Chris, this was my memory, too, but it's hard to imagine that it's exactly true: for the case $G=SU(2)$, $N=\mathbb{Z}/2$ and $G/T=P^1$, whose cohomology is indeed free of rank two. However there's no way that $W$ can act on it by the regular representation, since one generator is in dimension 0, and the other in dimension 2. | |
| Dec 20, 2012 at 20:15 | history | answered | Chris Gerig | CC BY-SA 3.0 |