Timeline for Are there cases in which the Weyl group _does_ act on the flag variety/springer fiber?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2021 at 15:29 | answer | added | Uri Bader | timeline score: 3 | |
| Jun 6, 2021 at 8:37 | comment | added | user148212 | ......, according to the Springer correspondence, the rep afforded by the cohom should be the 2-dim irrep of S_3. | |
| Jun 6, 2021 at 8:37 | comment | added | user148212 | It appears to me that the most simple example explaining the situation is the subregular Springer fibre (i.e. Springer fibre at a subregular unipotent element) of SL_3: In this case the Springer fibre is two lines intersected at a single point and the two lines form the two irreducible component, so, if you let the Weyl group S_3 act (continuously) on the Springer fibre, then it either preserves or exchanges the two components, and as a result, its induced action on the cohomology is either a multiple of the trivial rep or a sum of the trivial rep and the sign rep; however...... | |
| Jun 5, 2021 at 23:00 | review | First posts | |||
| Jun 6, 2021 at 6:53 | |||||
| Jun 5, 2021 at 22:55 | history | asked | Aaron Wild | CC BY-SA 4.0 |