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Chapter VI of my old Springer Lecture Notes in Mathematics 789 Arithmetic Groups (1980) is in English and gives a version of H. Matsumoto's and C. Moore's arguments for the subgroups of $\operatorname …

There are probably multiple ways to see that $G(\mathbb{R})$ is non-compact when $G$ is a Chevalley group (in either the narrow sense of Chevalley or the broader sense of Steinberg's lectures). One …

In the original sense, Chevalley groups are generated by copies of the additive group of the field and are in fact simple as abstract groups if the field is not too small. (This was the motive for …

I'm not quite sure what you are looking for, but Green's work (though combinatorial and influential) was only one of the inputs for the Deligne-Lusztig paper of 1976. It might help for example to …

Probably the earliest reference is the 1956-58 Chevalley seminar, available online in typed format, which has been republished in 2005 as a typeset book edited by P. Cartier: see Chapter 21. (No speci …

The basic answer to the question here is "Yes, there is a strong analogy via the Iwasawa decomposition for a semisimple Lie group". If I were trying to study this kind of question, I'd probably st …

This line of questioning has been pursued in greater generality. starting in prime characteristic by Ron Irving (and myself) and then in the analogous setting of category $\mathcal{O}$ for a semisimpl …

To expand on Marty's brief comment, self-duality is not possible for any $p$ and for many if not most finite groups. (Also, your tag 'lie-groups' is not meaningful here, since a finite group of rat …

This area of the subject is somewhat frustrating, since there is a lot of literature but not many satisfactory results involving the entire cohomology ring. For what it's worth, I'll point you to a …

For the finite groups GL$_n(\mathbb{F}_q)$ there is an early paper by Lusztig well worth checking out here. This predates his broader work on finite groups of Lie type with Deligne (1976), where they …

This is just a comment (in community-wiki format). I don't know how to cite an article efficiently otherwise. As YCor points out, this notion has become fairly standard in the development of Lie grou …

Here are some further comments, in community-wiki format. As earlier comments indicate, compact Lie groups and their maximal tori raise many questions. For instance, the real case is perhaps more …

This question was raised, both in characteristic 0 and in arbitrary characteristic, in back-to-back 2003 papers by R. Steinberg here and P. Chatterjee here. I recall reviewing these papers together …

The three questions asked are fairly elementary, as the comment by LSpice indicates; in the format here, it's best to avoid multiple questions however. Aside from this, it's probably more natural t …

As Paul Levy's answer suggests, your question probably needs some case-by-case work to be answered completely. The most general perspective may come from older work of Borel-Tits in their 1972 IHES …