Exceptional Reflection Groups, Varieties and Morphisms

This graduate text offers a guided tour through the remarkable world of exceptional finite complex reflection groups and their connections with algebraic geometry. Drawing on decades of research, the author develops a self-contained account that combines group theory, invariant theory, and geometry, emphasizing explicit constructions, concrete examples, and exceptional objects that illuminate the richness of the subject. After a concise review of the necessary background and the fundamental results on reflection groups and their invariants, the book focuses on the exceptional groups themselves. New and classical constructions are presented, together with the exceptional morphisms linking certain complex reflection groups to Coxeter groups. These methods provide fresh insight into the relationships between exceptional groups, their invariants, and the algebraic structures that surround them.

Throughout, the emphasis is on examples, computations, and geometric interpretations that complement standard references in the field. The book is prime for topics courses as well as advanced courses in finite reflection groups and invariant theory, to name just two. By bringing together material scattered across the literature and highlighting deep interactions between algebra and geometry through the notion of symmetry, this volume will be valuable to researchers in reflection groups and algebraic geometry, graduate students seeking rich examples, and mathematicians interested in exceptional phenomena.