Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results from the geometry of linear groups. The presented methods are applied to some geometric constructions non-related to buildings — Grassmannians of infinite-dimensional vector spaces and the sets of conjugate linear involutions.
The book is self-contained and the requirement for the reader is a knowledge of basic algebra and graph theory. This makes it very suitable for use in a course for graduate students.
Sample Chapter(s)
Chapter 1: Introduction (113 KB)
Contents:
- Linear Algebra and Projective Geometry
- Buildings and Grassmannians
- Classical Grassmannians
- Polar and Half-Spin Grassmannians
Readership: Students and researchers in graph theory and algebra.
