000			02818nam a22003137a 4500
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020			_a9781470412258
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	0	_a512.81 _bBOR-C
100	1		_aBorel, Armand
245	1	0	_aContinuous cohomology, discrete subgroups, and representations of reductive groups
250			_a2nd ed.
260			_aRhode Island : _bAmerican Mathematical Society, _c2000.
300			_axvii, 260p.
490			_aMathematical surveys and monographs, _x0076-5376 ; _vv. 67
504			_aIncludes bibliographical references (p. 253-258) and index.
520			_aThe 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 -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.
521			_aGraduate students and research mathematicians working in continuous cohomology.
650		0	_aLie groups.
650		0	_aRepresentations of groups.
650		0	_aHomology theory.
650		0	_aLanglands classification
700	1		_aWallach, Nolan R.
856			_uhttps://www.ams.org/bookstore/pspdf/surv-67-prev.pdf?_gl=1*1s10dl4*_ga*MTg3NTQ1NzY3LjE3MTEwOTIxMzU.*_ga_26G4XFTR63*MTcxNjM2MDUzNC42LjEuMTcxNjM2MDU0Mi4wLjAuMA.. _3Table of Contents
856			_uhttps://www.goodreads.com/book/show/62095530-continuous-cohomology-discrete-subgroups-and-representations-of-reduct?ref=nav_sb_ss_1_13#CommunityReviews _3Reviews
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