Download E-books Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups: Second Edition (Mathematical Surveys and Monographs) PDF

By A. Borel, N. Wallach

The ebook by way of Borel and Wallach is a vintage therapy of using cohomology in illustration thought, rather within the environment of automorphic kinds and discrete subgroups. The authors start with basic fabric, masking Lie algebra cohomology, in addition to non-stop and differentiable cohomology. a lot of the equipment is designed for the learn of the cohomology of in the neighborhood symmetric areas, discovered as double coset areas, the place the quotient is through a maximal compact subgroup and via a discrete subgroup. Such areas are crucial to functions to quantity idea and the research of automorphic varieties. The authors provide a cautious presentation of relative Lie algebra cohomology of admissible and of unitary -modules. As a part of the overall improvement, the Langlands type of irreducible admissible representations is given. Computations of significant examples are one other useful a part of the publication. within the 20 years among the 1st and moment variations of this paintings, there has been titanic development within the use of homological algebra to build admissible representations and within the research of mathematics teams. the second one version is a corrected and improved model of the unique, which was once an incredible catalyst within the development of the sector. along with the elemental fabric on cohomology and discrete subgroups found in the 1st variation, this version additionally comprises expositions of a few of an important advancements of the 2 intervening a long time.

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