Representations of Elementary Abelian p-Groups and Vector Bundles

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

David J. Benson (Author)

9781107174177, Cambridge University Press

Hardback, published 17 November 2016

348 pages, 5 b/w illus.
22.9 x 15.2 x 2.4 cm, 0.68 kg

'In summary, this book provides a thorough introduction to the theory of the correspondence between modular representations of elementary abelian groups and vector bundles over projective space. In it the reader will find results from the literature, as well as new contributions to the field. It provides all of the background necessary to understand the material, and provides a lot of interesting examples as well as open problems.' Alan Koch, Mathematical Reviews

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theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished research.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.

Subject Areas: Algebraic topology [PBPD], Algebraic geometry [PBMW], Groups & group theory [PBG], Algebra [PBF]