Timeline for $G^F$ conjugacy class of $F$-stable maximal tori, in an algebraic group $G$ defined over $\mathbb{F}_{q}$
Current License: CC BY-SA 4.0
7 events
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| Jun 1, 2019 at 21:44 | comment | added | Jim Humphreys | Sorry if my comments have been too superficial; but I wanted to emphasize that the history is compllicated, while your insistence on regular semisimple elements in the other question seems misleading and undermotivated (so I've been inclined to ignore that condition). Most of the theory comes originally from Borel-Tits and then Springer and Steinberg papers, whereas Carter's book is a serious attempt to write a thorough summary. | |
| May 30, 2019 at 23:22 | comment | added | Jim Humphreys | As you realize, the discussion in Chapter 3 of Carter's sprawling book answers your question affirmatively (and more). But most of this information comes from the long paper of Borel-Tits (1965) on reductive groups over am aritrary field, and the article by Springer-Steinberg in Lecture Notes 131 treats carefully the case of a finite field. where the group $G$ is either split or quasi-split. | |
| May 30, 2019 at 15:40 | comment | added | Riju | I got an answer to my question in the book “ Finite Groups of Lie type” by R. Carter. The answer is in Chapter 3, Pg 96-97. Maybe I’ll write a short answer to my question. | |
| May 28, 2019 at 21:40 | comment | added | Riju | Yeah I know the lecture notes you are talking about. I will have a look at it! | |
| May 28, 2019 at 20:59 | comment | added | Jim Humphreys | Have you looked at the long article by Springer and Steinberg in Lecture Notes in Mathematics 131 (or at the related work of Steinberg)? | |
| May 28, 2019 at 20:55 | history | edited | Jim Humphreys | CC BY-SA 4.0 |
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| May 28, 2019 at 14:29 | history | asked | Riju | CC BY-SA 4.0 |