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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (Paperback, 2nd Revised edition)
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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (Paperback, 2nd Revised edition)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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The book by Borel and Wallach is a classic treatment of the use of
cohomology in representation theory, particularly in the setting of
automorphic forms and discrete subgroups. The authors begin with
general material, covering Lie algebra cohomology, as well as
continuous and differentiable cohomology. Much of the machinery is
designed for the study of the cohomology of locally symmetric
spaces, realized as double coset spaces, where the quotient is by a
maximal compact subgroup and by a discrete subgroup. Such spaces
are central to applications to number theory and the study of
automorphic forms. The authors give a careful presentation of
relative Lie algebra cohomology of admissible and of unitary
$G$-modules. As part of the general development, the Langlands
classification of irreducible admissible representations is given.
Computations of important examples are another valuable part of the
book. In the twenty years between the first and second editions of
this work, there was immense progress in the use of homological
algebra to construct admissible representations and in the study of
arithmetic groups. The second edition is a corrected and expanded
version of the original, which was an important catalyst in the
growth of the field. Besides the fundamental material on cohomology
and discrete subgroups present in the first edition, this edition
also contains expositions of some of the most important
developments of the two intervening decades.
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