I am interested in an expository text in English, which summarizes the main results and aspects of the structure theory of reductive groups over local fields, in a hopefully not very technical manner (full proofs are not necessary, though sketches of the main arguments would be nice). Specifically covering the following topics:
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The apropriete BN-pair (with the Iwahori subgroup)
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The affine root system
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The affine Weyl group
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the Bruhat decomposition of the affine flag variety.
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Classification and structure of standard parabolic (or parahoric?) subgroups.
The emphasis is really being on readability and not thoroughness, so well written notes of some course or seminar on the subject would be great. I could not find any textbook on the subject, and the standard reference everywhere seems to be the original french papers of Bruhat and Tits from the 70's, but if there is such a textbook It would be optimal.
Another point is that I really don't know much about buildings, and even though It seems a fundamental part of the theory, It would be much easier for me to approach this at first from a direction not relaying heavily on the theory of buildings (if it is at all possible).
Finally, I am mostly interested in the case of the field $\mathbb{C}((t))$ (and not, say, $\mathbb{Q}_p$), which is not a local field in the strict sense (not locally compact), but is a complete non-archimedean DVR (which some people still call a local field), so I am looking for a source that applies for this case.
Best Answer
http://www.math.umn.edu/~garrett/m/buildings/book.pdf
was derived from seminar notes on structure of split classical p-adic groups, intending to circumvent the larger apparatus of algebraic groups and buildings. It became clear in the original project that it was necessary to develop some aspects of buildings, since they encapsulated and packaged-up some otherwise-clumsy (if not intractable) issues.
For split classical groups, it is possible to develop the building-theory "directly" (as J. Tits did, too, before the general development) in terms of flags of subspaces and flags of lattices (with additional structure...)
Edit: also, a smaller, newer treatment of buildings without Coxeter group stuff intervening is at http://www.math.umn.edu/~garrett/m/v/bldgs.pdf