Leírás
Buildings are special simplicial complexes on which certain classical groups act in an illuminating way. The idea is to deduce results in group theory and representation theory by geometric arguments. In this introductory talk I recall the notion of buildings and give examples. The most common example is the Bruhat-Tits tree which is the $(p+1)$-regular (infinite) tree. The spherical building of $GL_n$ (over any field) can be used to define parabolic subgroups and prove the Bruhat decomposition. I also introduce the Bruhat-Tits building of $GL_n$ over a (nonarchimedean) local field as a common generalization of the spherical building and the Bruhat-Tits tree. If time permits, I will indicate how the contractibility of the Bruhat-Tits building leads to resolutions of smooth admissible representations of the group (a result of Schneider and Stuhler).