The illustration thought of reductive algebraic teams and comparable finite reductive teams has many purposes. The articles during this quantity supply introductions to numerous features of the topic, together with algebraic teams and Lie algebras, mirrored image teams, abelian and derived different types, the Deligne-Lusztig illustration idea of finite reductive teams, Harish-Chandra idea and its generalizations, quantum teams, subgroup constitution of algebraic teams, intersection cohomology, and Lusztig's conjectured personality formulation for irreducible representations in leading attribute. The articles are conscientiously designed to augment each other, and are written by way of a workforce of exceptional authors: M. Broué, R. W. Carter, S. Donkin, M. Geck, J. C. Jantzen, B. Keller, M. W. Liebeck, G. Malle, J. C. Rickard and R. Rouquier. This quantity as an entire may still offer a really obtainable advent to a huge, although technical, topic.
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