Reference request: expository text on the structure of reductive groups over non-archimedean local fields

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


The standard (classical) survey is:

Tits, J. Reductive groups over local fields. Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, pp. 29--69, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979.

But it is still quite difficult. The following lectures are a helpful complement:

Yu, Jiu-Kang Bruhat-Tits theory and buildings. Ottawa lectures on admissible representations of reductive $p$-adic groups, 53--77, Fields Inst. Monogr., 26, Amer. Math. Soc., Providence, RI, 2009.


A very nice exposition is given in I.G. Macdonalds Spherical functions on a group of p-adic type

Another nice exposition is given in the section 3 of the these notes.

Garret's book is perfect for learning about buildings in general, while these notes summarize exactly how they one constructs a building for a reductive group.