By A. Borel, N. Wallach

The e-book by way of Borel and Wallach is a vintage therapy of using cohomology in illustration concept, really within the atmosphere of automorphic types and discrete subgroups. The authors start with basic fabric, overlaying Lie algebra cohomology, in addition to non-stop and differentiable cohomology. a lot of the equipment is designed for the research of the cohomology of in the neighborhood symmetric areas, discovered as double coset areas, the place the quotient is by way of a maximal compact subgroup and by way of a discrete subgroup. Such areas are valuable to purposes to quantity idea and the research of automorphic kinds. The authors supply a cautious presentation of relative Lie algebra cohomology of admissible and of unitary -modules. As a part of the final improvement, the Langlands class of irreducible admissible representations is given. Computations of significant examples are one other helpful a part of the booklet. within the 20 years among the 1st and moment variations of this paintings, there has been giant growth 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 multiplied model of the unique, which used to be a huge catalyst within the progress of the sphere. in addition to the elemental fabric on cohomology and discrete subgroups found in the 1st variation, this variation additionally includes expositions of a few of crucial advancements of the 2 intervening a long time.

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