Timeline for Points on Deligne-Lusztig varieties: Interpreting Borels in relative position as flags with conditions
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2012 at 14:14 | comment | added | Jim Humphreys | @Dror: To clarify further, Lusztig is working with a special set-up just for certain classical linear groups. One Weyl group might be a subgroup of another (fixed by a twisted Frobenius map); thus a Coxeter element (in Steinberg's twisted sense) would be defined relative to the larger Weyl group, etc. The paper has lots of ad hoc notation and may or may not be a useful place to start. It was published in Proc. LMS 33 (1976) at a very early stage of what turned out to be a vast project to find all character values of finite groups of Lie type. This paper focuses on a "Coxeter torus". | |
| Jul 10, 2012 at 7:34 | vote | accept | Dror Speiser | ||
| Jul 10, 2012 at 5:51 | answer | added | Ben Webster♦ | timeline score: 5 | |
| Jul 9, 2012 at 23:00 | comment | added | Dror Speiser | I am aware of this fact, and it confuses me as well. The words "a Coxeter element of minimal length" are in the third paragraph of the article I cite. | |
| Jul 9, 2012 at 22:56 | comment | added | Jim Humphreys |
A small question about the formulation: What do you mean by "a Coxeter element of minimal length"? In a finite Coxeter group such as a Weyl group, all Coxeter elements $w$ have the same length (equal to the rank of the given group) and are conjugate. I'll have to look at the original papers to sort out better what is going on here, but the terminology confuses me at first.
|
|
| Jul 9, 2012 at 22:43 | history | asked | Dror Speiser | CC BY-SA 3.0 |