Representations of Elementary Abelian p-Groups and Vector Bundles

Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups. This is the first book to offer a detailed study of the representation theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished research. Special attention is given to recent work on modules of constant Jordan type, and the methods involve producing and examining vector bundles on projective space and their Chern classes. Extensive background material is provided, which will help the reader to understand vector bundles and their Chern classes from an algebraic point of view, and to apply this to modular representation theory of elementary abelian groups. The final section, addressing problems and directions for future research, will also help to stimulate further developments in the subject. With no similar books on the market, this will be an invaluable resource for graduate students and researchers working in representation theory.

Preface; Introduction; 1. Modular representations and elementary abelian groups; 2. Cyclic groups of order p; 3. Background from algebraic geometry; 4. Jordan type; 5. Modules of constant Jordan type; 6. Vector bundles on projective space; 7. Chern classes; 8. Modules of constant Jordan type and vector bundles; 9. Examples; 10. Restrictions coming from Chern numbers; 11. Orlov's correspondence; 12. Phenomenology of modules over elementary abelian p-groups; A. Modules for Z/p; B. Problems; References; Index.

David J. Benson is currently the Sixth Century Professor of Mathematics at the University of Aberdeen. He has authored a number of books, including Representations and Cohomology (Cambridge, 1991) and Polynomial Invariants of Finite Groups (Cambridge, 1993).