Timeline for Borel's presentation for the cohomology of a Flag Variety
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| S Mar 7, 2019 at 17:57 | history | suggested | Phil Tosteson | CC BY-SA 4.0 |
fixed target of Bi^*
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| Mar 7, 2019 at 17:48 | review | Suggested edits | |||
| S Mar 7, 2019 at 17:57 | |||||
| Mar 7, 2019 at 16:09 | comment | added | DCT | 1) Is there a reference for the statement that the W-invariants form a polynomial ring when k has positive characteristic? I have looked and found related statements, but not that one. For Sn I think it holds integrally. 2) Your proof shows that the integral cohomology is always generated on degree 2. However, I was unable to see how this agrees with Knutson's answer linked in the question. The Chow ring of BG agrees with the W-invariants of the Chow ring of BT for G special (Edidin's characteristic classes paper). Apologies in advance for mistakes (typing on a cell phone before a flight). | |
| Mar 7, 2019 at 15:15 | comment | added | Jason Starr | I am just clarifying your claim: "Miraculously, $H^*(BT;k)^W$ is always polynomial, and $H^*(BT;k)$ is a free module (of rank $|W|$) over this invariant ring." I assume that you mean that this works if $k$ has characteristic $0$. In that case, this follows from the Chevalley-Shephard-Todd theorem. When $k$ has characteristic $2$ and $W$ is $\mathfrak{S}_2$, this cannot hold. | |
| Mar 7, 2019 at 14:47 | history | answered | Nicholas Kuhn | CC BY-SA 4.0 |