Math 765: Buildings and Classical Groups


Announcements:


What? Linear reflection groups; affine reflection groups. Coxeter groups; Coxeter complexes. Spherical buildings; groups with a BN-pair. Classical groups.


When? Monday 12.40-13.30 (M-214)
Wednesday 10.40-12.30 (M-231)


Main Books.


Other Books.


In the Class.

Week 1: (2 hours) Introduction to finite reflection groups. Root systems, simple systems, simple reflections.
Week 2: The deletion condition. An equivalent condition for being a Coxeter group. Coxeter graphs. Classification of finite reflection groups.
Week 3: A quick review of affine reflection groups. The geometrization of Coxeter groups.
Week 4: Generalized reflections. Exchange and Deletion Conditions. Bruhat ordering in Coxeter groups.
Week 5: Parabolic subgroups in Coxeter groups. Chamber complexes and foldings.
Week 6: No lectures, because of the holiday.
Week 7: Coxeter complexes.
Week 8: No lectures, because of a conference.
Week 9: Characterization of Coxeter complexes by walls. (Presentation by Erkan M. T�rkan)
Week 10: Characterization of Coxeter complexes by walls (continued). (Presentation by Yal��n Karata�)
Week 11: (2 hours) Buildings (definitions, examples, preliminaries).
Week 12: Labels, apartment systems, spherical buildings.
Week 13: A group of label-preserving simplicial isomorphisms acting stongly transistively on a (thick) building is a BN-pair.
Week 14: Parabolic subgroups, generalized BN-pairs. (Presentation by G�khan Benli)
Week 15: Parabolics and Levi components in the spherical case. (Presentation by G�khan Benli)
Week 15+1: Buildings from BN-pairs (Presentation by Hakan G�nt�rk�n)


This line last updated on 13 January 2007.