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Unlike many other terms in mathematics which have a universally understood meaning (for instance, "group"), the term classical group seems to have a fuzzier definition. Apparently it originates with …

Some of what's been said so far about the history makes good sense, but by no means all. Let me add my own perspective, for what it's worth. The font called Fraktur by LaTeX (also known as "gothic …

Steinberg's lecture at the 1966 ICM in Moscow here surveyed his work on regular elements of semisimple algebraic groups, while also formulating a number of then-open questions as "problems" (with posi …

This question was motivated by a more general question raised by Jan Weidner here. In general one starts with a variety $X$ (say smooth) over an algebraic closure of a finite field $\mathbb{F}_q$ of …

To supplement what Pete says, I'd emphasize that "root systems" have been defined in a variety of ways for a variety of purposes related to Lie theory or to some type of "reflection" group. (For in …

Start with the Dynkin diagram of an irreducible root system, typically associated with a simple Lie algebra over $\mathbb{C}$ or a simple algebraic group. Most of the simply-laced ADE diagrams admi …

One classical source for the case $n=2$, with somewhat old-fashioned notation for some of the related groups, is a paper by Richard Brauer and his student Cecil Nesbitt: On the modular characters of g …

Classification of nilpotent Lie algebras in characteristic 0 is an old problem, with a lot of literature. For the dimensions up to 6 there is a finite list. Among the many relevant papers on MathSci …

By now there is a fairly long paper trail dealing with this kind of question, which is usually a byproduct of the study of representation theory over rings of $p$-adic integers, etc. I'm not aware of …

In characteristic 0 or good prime characteristic, there are standard ways to relate the unipotent variety $\mathcal{U}$ of a simple algebraic group $G$ and the nilpotent variety $\mathcal{N}$ of its L …

Since the decomposition of tensor products has a complicated history, it's worth adding some comments to ARupinski's answer. 1) Though Weyl's character formula is fundamental for finite dimensional …

Keeping in mind that a generating set of invariant polynomials having the required degrees is not unique, various computations have been recorded in the literature. Those I was aware of before 1990 …

Probably the earliest intrinsic definition of Weyl group occurs in section 1.2 of the groundbreaking paper "Representations of Reductive Groups Over Finite Fields" by Deligne and Lusztig (Ann. of Math …

This is a follow-up to a recent mathoverflow question 34387 about computing the orders of finite unitary groups and the comments made there. Between 1955 (Chevalley's Tohoku paper) and 1968 (Steinbe …

Given a simple Lie algebra over an algebraically closed field of good characteristic such as $\mathbb{C}$, its subvariety $\mathcal{N}$ of nilpotent elements has dimension $2N$ (where $N$ is the num …