Bruhat–Tits buildings Part 2: Petra Schwer

This mini-course covers constructions of Bruhat-Tits buildings as well es some of their geometric and combinatorial properties. Buildings are geometric objects associated with reductive groups over non-archimedian local fields potentially with a discrete valuation. We will see explicit constructions of Bruhat-Tits buildings, axiomatic descriptions and the connection to BN-pairs. The most important geometric features of a building are its apartments and retractions onto apartments, which will also be introduced in the course.

Furthermore it will be explained how the geometry of retractions and the combinatorics of folded galleries provides a unified framework to study orbits in affine flag varieties. When X is a Bruhat-Tits building for a group over a local field, we can then relate labeled folded galleries and shadows to double coset intersections in affine flag varieties. This will allow us to hint at connections with the Hecke algebras discussed in Anne-Marie Aubert's course.

Notes 1: https://algebra.ugent.be/hdx/files/No...
Notes 2: https://algebra.ugent.be/hdx/files/No...
Notes 3: https://algebra.ugent.be/hdx/files/No...