But such a cool-looking paper!

Either that's a bizarre TeX error, or else I have a new entry for the question mathoverflow.net/questions/18593/…

en.wikipedia.org/wiki/Minuscule_representation

The reference of (my) choice is Richardson, Rohrle, Steinberg, "Parabolic subgroups with abelian unipotent radical," in Inventiones v.110, no. 3 (1992), p. 649-671.

I like using "such that" (i.e., \text{such that}) whenever there's room for it. And with semicolons, it might seem like the paper is sadly winking );

Way too broad a question for my taste. It's good the OP realized that older math books could be worthwhile, but asking for a list is kind of like asking for "the greatest books of all time". There are just too many. But criticism aside, I found my horizons broadened by "The Mathematics of Egypt, Mesopotamia, China, India, and Islam," edited by V. Katz. That's where I first realized that I could read and enjoy much older math texts, especially those from outside the Eurocentric canon. You could start with Katz's book as a source for excerpts, and look up full books when interested.

@Mariano: Not really. I guess my point is that matrix algebras are in general endomorphism rings of vector spaces -- the 2x2 case is just one example of the infinite family of examples of type $A_n$. But the octonions are really connected to $G_2$ -- no way around it, no easy shortcuts. I would still say that Zorn's split octonions are simpler than the non-split octonions. For example, identifying a maximal order in the non-split octonions is difficult (due to Coxeter after earlier mistakes), but the maximal order in the split octonions is the obvious choice.

@Mariano, I think the issue you're describing is that most mathematicians are happy to live without the octonions and exceptional groups. Matrix algebras and $GL_n$ (and classical groups) are sufficient for most people's work. The octonions and $G_2$ are not so universally studied, and maybe people think they are more difficult than they really are. I don't think Zorn's model of the split octonions (over $Z$) is too bad at all -- just 2x2 matrices with vectors in $Z^3$ off the diagonal. Hard to get much simpler than Zorn, I think.

First, I don't think that representations are coming from nowhere. When a group $G$ acts on a space $X$, and you have a $G$-equivariant bundle on the space $X$, then you get a representation of $G$ on the sections (and higher cohomology) of the bundle. Maybe the most impressive results beyond the theorem itself are how useful it is for generalizations. The generalization that comes first to my mind is Schmid's "L²-cohomology and the discrete series" (Annals, 1976) which proved a conjecture of Langlands by using a geometric realization in the spirit of Borel-Weil-Bott.

"I assume that the ancient Greeks had an idea of a complete normed space (${\mathbb R}$ and ${\mathbb R}^2$ would be enough for our purposes for quite a while), a set, a linear transformation, and the center of mass." Really? Really??!