Search Results

The classical viewpoint is captured well in the 1962 book Representation Theory of Finite Groups and Associative Algebras by Curtis and Reiner (Wiley), Corollary 29.15. This of course doesn't direc …

As Derek Holt comments, cohomology has complications even for fimite general linear groups. Probably you are using the term "reductive" too casually and should replace it by "simple" or perhaps "semis …

First of all, I'd inquire what role the characteristic of the field plays here. It's true that the finite twisted groups rely on characteristics 2, 3 especiallu, but infinite twisted groups include …

YCor's question about your definition of "nilpotent" is definitely in order, because Borel and Springer already defined this term in general for affine (=linear) algebraic groups over an arbitrary inf …

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 …

This is just a comment but in community wiki format. Most studies of semisimple (or reductive) algebraic groups and finite groups of Lie type emphasize counting the number of classes of various el …

Over an algebraically closed field (of any characteristic), it is fairly obvious using the omitted definition of "standard parabolic" that the assertion here for a pair of included standard parabolics …

First of all, it's probably intended that "linear algebraic groups" are semisimple or at least reductive (and connected). For example, a solvable group might have no semisimple elements except 1 (et …

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 …

No, your parenthetic comment at the end indicates some confusion about the nature of Deligne-Lusztig virtual (= generallized) characters: these are defined to be $\mathbb{Z}$-linear combinations of ac …

To me the question itself (and the answers) are out of focus, starting with the claim that the ring of Weyl group invariants is somehow central. Chevalley's 1955 argument does show that this ring is …

To answer your question, it's enough to point out that every root (in a reduced root system such as $\Phi$) plays the role of simple root in some basis $\Delta$. Note however that some absolute root …

Concerning your Q1, it may be of interest to fill in some of the background due to Steinberg (which in turn had a lot of influence on Springer's work). In his 1966 ICM talk, Steinberg formulated quit …