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EDIT: After looking into the history more closely, I think it's fairly certain that the correct answer to the question is Calvin Moore. (See my added text below.) The question is interesting and l …

There has been a lot of systematic study in recent decades of the maximal subgroups of finite simple groups, especially groups of Lie type. This goes far beyond the special case here, but is written …

This is an extended comment, certainly not an answer to the very broad and perhaps unanswerable multiple part question being asked here ("How did people find those varieties?"). A facetious response …

As Olivier's answer indicates, a direct approach to the computation using classical techniques of Sah and others is possible in a small isolated case like this. But it's a good idea to be aware of s …

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 …

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 …

It's hard to keep track of all relevant literature on the inverse Galois problem for finite groups of Lie type, but at this point many special cases have been worked out while others remain open. On …

Without offering a complete answer to the stated question, I'd first ask what significance the answer would have (one way or the other) in terms of Lie theory? I'd also want to extract the essential …

As the discussion shows, there really isn't any explicit construction which works for all primes $p$. (Here you really want to specify that $p$ is odd, however, to avoid trivialities.) It may or ma …

It's easy to embed the (cyclic) multiplicative group of a finite field into the multiplicative group of $\mathbb{C}$ (or other algebraically closed field of characteristic 0): assign to a generator of …

Let me add a couple of things to what grghxy has said. 1) The study of these groups over $\mathbb{Z}$ has been complicated, going back to Chevalley's work and Borel's lecture notes (which aren't quit …

To reinforce what's already been said and add some references, I'd emphasize first that Harish-Chandra's "philosophy of cusp forms" was indeed a driving force in the study of representations over both …

The Paris lectures, along with others he gave later, were spliced together into a publication: Introduction aux groupes arithmetiques (softcover, Hermann, Paris, 1969). As his nominal assistant at …

Maybe it's worth pointing out that the question contained in the header has an obvious negative answer (and is not the main question being asked). The easiest counterexample would be the product of t …

I've never seen an authoritative explanation for the choice of the lower case letter $\ell$ or $l$ to denote an arbitrary prime different from a given prime $p$. This now has its own LaTeX command \e …