The Geometry of the Classical Groups

The author starts with the introduction of vector spaces, sesquilinear forms, and then studies the classical groups - special linear, symplectic, unitary and orthogonal groups - along the lines of E. Artin. Emphasis is placed on the "building" of the groups and their corresponding BN-pairs. Symplectic groups, unitary groups, orthogonal groups, and the Klein correspondance are thoroughly treated in individual chapters, each offering an abundance of exercises for deepening the understanding. "It is therefore highly recommended to students beginning to work with classical groups and who want to get some knowledge about the interaction between groups, classical geometries, buildings, BN-pairs and modern treatments like diagram geometries. ... The book is carefully written. ... The book fills a gap in the existing literature." (G. Stroth, Zentralblatt f. Mathematik).