These lectures from the August 1994 European School of Group Theory summer session introduce different perspectives on reductive groups, namely: modular representations of algebraic groups and relations to quantum groups, orbital varieties, Goldie rank polynomials, and unitary highest weight modules, discontinuous groups and Clifford-Klein forms of pseudo-Riemannian homogeneous manifolds, the method of stationary phase and applications to geometry and analysis on Lie groups, and the orbit method and unitary representations for reductive Lie groups. The subject requires a broad knowledge of mathematics, and will be of interest to students and researchers who wish to see some of the classical techniques that have opened up new avenues of research. Annotation c. by Book News, Inc., Portland, Or.
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