This is the proceedings of a symposium on modular representation theory, held at the University of Virginia in 1998. Its main topics include:

(1) the modular representation theory of groups of Lie type in non-defining characteristic;

(2) the relationship of q-Schur algebras to quantisation of other algebras;

(3) connections with modular representation theory of symmetric groups;

(4) Broué’s conjectures on the equivalence of derived categories of modules in blocks with abelian defect group.

The first part of the book contains three comprehensive surveys on recent developments, stressing functorial and q-Schur algebra methods – by M. Geck on (1) and (2), J. Brundan and S. Kleshchev on (3), and R. Rouquier on (4). The second part comprises research papers dealing with particular aspects of the theory, by R. Boltje (a new reformulation of Alperin’s weight conjecture), M. Cabanes and J. Rickard (Broué’s conjecture on the Alvis-Curtis duality), S. R. Doty, D. K. Nakano, J. Du, C. Hoffman, N. J. Kuhn, K. Maagard and P. H. Tiep.

The book will serve as an invaluable source of recent progress in modular representation theory, both for established researchers and for graduate students.

Reviewer:

jtrl