The representations of a finitely generated team in a topological workforce $G$ shape a topological house that is an analytic type if $G$ is a Lie workforce, or an algebraic kind if $G$ is an algebraic crew. The research of this region attracts from and contributes to a variety of mathematical topics: algebra, research, topology, differential geometry, illustration concept, or even mathematical physics. occasionally, the distance of representations is the article of the research, in others it's a instrument in a application of research, and, in lots of situations, it's either. lots of the papers during this quantity are in response to talks introduced on the AMS-IMS-SIAM summer time learn convention at the Geometry of team Representations, held on the collage of Colorado in Boulder in July 1987.The convention was once designed to collect researchers from the varied components of arithmetic regarding areas of team representations. according to the spirit of the convention, the papers are directed at nonspecialists, yet comprise technical advancements to carry the topic to the present learn frontier. a few of the papers contain solely new effects. Readers will achieve an realizing of the current country of study within the geometry of staff representations and their purposes.
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